Journal ArticleRevue des maladies respiratoires · January 2024
In adults and teenagers, airway clearance physiotherapy techniques (ACPT) are various and numerous. However, they for still awaiting scientific validation. Among ACPTs, Slow Expiration with the Glottis Opened in the Lateral Posture (ELTGOL), Autogenic Drai ...
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Journal ArticleApplied and Computational Harmonic Analysis · September 1, 2023
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization scheme for recons ...
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Journal ArticleIEEE Transactions on Information Theory · January 1, 2023
In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there exists a variety of r ...
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Journal ArticleIEEE transactions on image processing : a publication of the IEEE Signal Processing Society · January 2023
X-radiography (X-ray imaging) is a widely used imaging technique in art investigation. It can provide information about the condition of a painting as well as insights into an artist's techniques and working methods, often revealing hidden information invi ...
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Chapter · January 1, 2023
Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. It consists in constructing a spectral parametrization for the manifo ...
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Journal ArticleConstructive Approximation · February 1, 2022
This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers. The results most commonly found in the literature prove that neural networks approx ...
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Journal ArticleIEEE transactions on image processing : a publication of the IEEE Signal Processing Society · January 2022
In this paper, we focus on X-ray images (X-radiographs) of paintings with concealed sub-surface designs (e.g., deriving from reuse of the painting support or revision of a composition by the artist), which therefore include contributions from both the surf ...
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Journal ArticlePaleobiology · November 27, 2021
The morphological and ecological diversity of lemurs and lorisiformes once rivaled that of the rest of the primate order. Here, we assemble a dataset of 3D models representing the second mandibular molars of a wide range of extant and fossil strepsirrhines ...
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Journal ArticleApplied and Computational Harmonic Analysis · November 1, 2021
In this paper, we study the stability of phase retrieval problems via a family of locally stable phase retrieval frame measurements in Banach spaces, which we call “locally stable and conditionally connected” (LSCC) measurement schemes. For any signal f in ...
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Journal ArticleInformation and Inference · June 1, 2021
We address the structure identification and the uniform approximation of sums of ridge functions f(x)=∑ i=1m gi(ai,x) on Rd, representing a general form of a shallow feed-forward neural network, from a small number of query samples. Higher order differenti ...
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Journal ArticleBMC ecology and evolution · April 2021
BackgroundLemurs once rivalled the diversity of rest of the primate order despite thier confinement to the island of Madagascar. We test the adaptive radiation model of Malagasy lemur diversity using a novel combination of phylogenetic comparative ...
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ConferenceEuropean Signal Processing Conference · January 1, 2021
X-ray images are widely used in the study of paintings. When a painting has hidden sub-surface features (e.g., reuse of the canvas or revision of a composition by the artist), the resulting X-ray images can be hard to interpret as they include contribution ...
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Journal ArticleIEEE Journal on Selected Areas in Information Theory · May 1, 2020
To help understand the underlying mechanisms of neural networks (NNs), several groups have studied the number of linear regions l of piecewise linear (PwL) functions, generated by deep neural networks (DNN). In particular, they showed that l can grow expon ...
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ConferenceICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings · May 1, 2020
X-radiography is a widely used imaging technique in art investigation, whether to investigate the condition of a painting or provide insights into artists' techniques and working methods. In this paper, we propose a new architecture based on the use of 'co ...
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Journal ArticleFoundations of Computational Mathematics · August 15, 2019
The problem of phase retrieval is to determine a signal f∈ H, with H a Hilbert space, from intensity measurements | F(ω) | , where F(ω) : = ⟨ f, φω⟩ are measurements of f with respect to a measurement system (φω)ω∈Ω⊂H. Although phase retrieval is always st ...
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Journal ArticleScience advances · August 2019
X-ray images of polyptych wings, or other artworks painted on both sides of their support, contain in one image content from both paintings, making them difficult for experts to "read." To improve the utility of these x-ray images in studying these artwork ...
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Journal ArticleMethods in Ecology and Evolution · April 1, 2019
Shape characterizers are metrics that quantify aspects of the overall geometry of a three-dimensional (3D) digital surface. When computed for biological objects, the values of a shape characterizer are largely independent of homology interpretations and of ...
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Journal ArticleProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition · December 14, 2018
Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing overfitting are data-inde ...
Full textCite

Journal ArticleRevue des maladies respiratoires · January 2024
In adults and teenagers, airway clearance physiotherapy techniques (ACPT) are various and numerous. However, they for still awaiting scientific validation. Among ACPTs, Slow Expiration with the Glottis Opened in the Lateral Posture (ELTGOL), Autogenic Drai ...
Full textCite

Journal ArticleApplied and Computational Harmonic Analysis · September 1, 2023
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization scheme for recons ...
Full textCite

Journal ArticleIEEE Transactions on Information Theory · January 1, 2023
In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there exists a variety of r ...
Full textCite

Journal ArticleIEEE transactions on image processing : a publication of the IEEE Signal Processing Society · January 2023
X-radiography (X-ray imaging) is a widely used imaging technique in art investigation. It can provide information about the condition of a painting as well as insights into an artist's techniques and working methods, often revealing hidden information invi ...
Full textCite

Chapter · January 1, 2023
Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. It consists in constructing a spectral parametrization for the manifo ...
Full textCite

Journal ArticleConstructive Approximation · February 1, 2022
This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers. The results most commonly found in the literature prove that neural networks approx ...
Full textCite

Journal ArticleIEEE transactions on image processing : a publication of the IEEE Signal Processing Society · January 2022
In this paper, we focus on X-ray images (X-radiographs) of paintings with concealed sub-surface designs (e.g., deriving from reuse of the painting support or revision of a composition by the artist), which therefore include contributions from both the surf ...
Full textCite

Journal ArticlePaleobiology · November 27, 2021
The morphological and ecological diversity of lemurs and lorisiformes once rivaled that of the rest of the primate order. Here, we assemble a dataset of 3D models representing the second mandibular molars of a wide range of extant and fossil strepsirrhines ...
Full textCite

Journal ArticleApplied and Computational Harmonic Analysis · November 1, 2021
In this paper, we study the stability of phase retrieval problems via a family of locally stable phase retrieval frame measurements in Banach spaces, which we call “locally stable and conditionally connected” (LSCC) measurement schemes. For any signal f in ...
Full textOpen AccessCite

Journal ArticleInformation and Inference · June 1, 2021
We address the structure identification and the uniform approximation of sums of ridge functions f(x)=∑ i=1m gi(ai,x) on Rd, representing a general form of a shallow feed-forward neural network, from a small number of query samples. Higher order differenti ...
Full textCite

Journal ArticleBMC ecology and evolution · April 2021
BackgroundLemurs once rivalled the diversity of rest of the primate order despite thier confinement to the island of Madagascar. We test the adaptive radiation model of Malagasy lemur diversity using a novel combination of phylogenetic comparative ...
Full textCite

ConferenceEuropean Signal Processing Conference · January 1, 2021
X-ray images are widely used in the study of paintings. When a painting has hidden sub-surface features (e.g., reuse of the canvas or revision of a composition by the artist), the resulting X-ray images can be hard to interpret as they include contribution ...
Full textCite

Journal ArticleIEEE Journal on Selected Areas in Information Theory · May 1, 2020
To help understand the underlying mechanisms of neural networks (NNs), several groups have studied the number of linear regions l of piecewise linear (PwL) functions, generated by deep neural networks (DNN). In particular, they showed that l can grow expon ...
Full textOpen AccessCite

ConferenceICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings · May 1, 2020
X-radiography is a widely used imaging technique in art investigation, whether to investigate the condition of a painting or provide insights into artists' techniques and working methods. In this paper, we propose a new architecture based on the use of 'co ...
Full textCite

Journal ArticleFoundations of Computational Mathematics · August 15, 2019
The problem of phase retrieval is to determine a signal f∈ H, with H a Hilbert space, from intensity measurements | F(ω) | , where F(ω) : = ⟨ f, φω⟩ are measurements of f with respect to a measurement system (φω)ω∈Ω⊂H. Although phase retrieval is always st ...
Full textCite

Journal ArticleScience advances · August 2019
X-ray images of polyptych wings, or other artworks painted on both sides of their support, contain in one image content from both paintings, making them difficult for experts to "read." To improve the utility of these x-ray images in studying these artwork ...
Full textOpen AccessCite

Journal ArticleMethods in Ecology and Evolution · April 1, 2019
Shape characterizers are metrics that quantify aspects of the overall geometry of a three-dimensional (3D) digital surface. When computed for biological objects, the values of a shape characterizer are largely independent of homology interpretations and of ...
Full textCite

Journal ArticleProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition · December 14, 2018
Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing overfitting are data-inde ...
Full textCite

Journal ArticleJournal of Fourier Analysis and Applications · June 1, 2018
We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work (Yin, in: Proceeding ...
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Journal ArticleAnat Rec (Hoboken) · April 2018
Automated geometric morphometric methods are promising tools for shape analysis in comparative biology, improving researchers' abilities to quantify variation extensively (by permitting more specimens to be analyzed) and intensively (by characterizing shap ...
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Journal ArticleJournal of Fourier Analysis and Applications · December 1, 2017
In this paper we consider the following problem of phase retrieval: given a collection of real-valued band-limited functions {ψλ}L2(Rd) that constitutes a semi-discrete frame, we ask whether any real-valued function f∈ L2(Rd) can be uniquely recovered from ...
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ConferenceIEEE transactions on image processing : a publication of the IEEE Signal Processing Society · February 2017
In support of art investigation, we propose a new source separation method that unmixes a single X-ray scan acquired from double-sided paintings. In this problem, the X-ray signals to be separated have similar morphological characteristics, which brings pr ...
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Journal ArticleSIAM Journal on Imaging Sciences · January 1, 2017
We propose an image representation scheme combining the local and nonlocal characterization of patches in an image. Our representation scheme can be shown to be equivalent to a tight frame constructed from convolving local bases (e.g., wavelet frames, disc ...
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Journal ArticleImage Processing On Line · January 1, 2017
We address the problem of mitigating the visually displeasing effects of cradling in X-ray images of panel paintings. The proposed algorithm consists of three stages. In the first stage the location of the cradling is detected semi-automatically and the gr ...
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Chapter · January 1, 2017
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the idea of iteratively ...
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Journal ArticleMethods of information in medicine · October 2016
BackgroundWith recent advances in sensor and computer technologies, the ability to monitor peripheral pulse activity is no longer limited to the laboratory and clinic. Now inexpensive sensors, which interface with smartphones or other computer-bas ...
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Journal ArticleThe American journal of cardiology · September 2016
The association between the J wave, a key component of the early repolarization pattern, and adverse cardiovascular outcomes remains unclear. Inconsistencies have stemmed from the different methods used to measure the J wave. We examined the association be ...
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Journal ArticleSIAM Journal on Imaging Sciences · August 30, 2016
We propose an algorithm that removes the visually unpleasant effects of cradling in X-ray images of panel paintings, with the goal of improving the X-ray image readability by art experts. The algorithm consists of three stages. In the first stage the locat ...
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Journal ArticleInverse Problems · August 5, 2016
About two decades ago, the concept of sparsity emerged in different disciplines such as statistics, imaging, signal processing and inverse problems, and proved to be useful for several applications. Sparsity-enforcing constraints or penalties were then sho ...
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ConferenceProceedings - International Conference on Image Processing, ICIP · August 3, 2016
In support of art investigation, we propose a new source separation method that unmixes a single X-ray scan acquired from double-sided paintings. Unlike prior source separation methods, which are based on statistical or structural incoherence of the source ...
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ConferenceICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings · May 18, 2016
We consider the problem of recognizing objects in collections of art works, in view of automatically labeling, searching and organizing databases of art works. To avoid manually labelling objects, we introduce a framework for transferring a convolutional n ...
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Journal ArticlePhilosophical transactions. Series A, Mathematical, physical, and engineering sciences · April 2016
A new method is proposed to determine the time-frequency content of time-dependent signals consisting of multiple oscillatory components, with time-varying amplitudes and instantaneous frequencies. Numerical experiments as well as a theoretical analysis ar ...
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Journal ArticleIEEE Signal Processing Letters · November 1, 2015
We study Sigma-Delta (Σ Δ) quantization of oversampled bandlimited functions. We prove that digitally integrating blocks of bits and then down-sampling, a process known as decimation, can efficiently encode the associated Σ Δ bit-stream. It allows a large ...
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Journal ArticleIEEE Signal Processing Magazine · July 1, 2015
Hanging in the Saint Bavo Cathedral in Ghent, Belgium, is The Ghent Altarpiece, also known as The Adoration of the Mystic Lamb (see Figure 1). According to an inscription on the outer frames, it was painted by brothers Hubert and Jan van Eyck for Joos Vijd ...
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Journal ArticleSignal Processing Magazine, IEEE · July 2015
Quantitative canvas weave analysis has many applications in art investigations of paintings, including dating, forensics, and canvas rollmate identification. Traditionally, canvas analysis is based on X-radiographs. Prior to serving as a painting canvas, a ...
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Journal ArticleIEEE transactions on pattern analysis and machine intelligence · February 2015
Super-resolution methods form high-resolution images from low-resolution images. In this paper, we develop a new Bayesian nonparametric model for super-resolution. Our method uses a beta-Bernoulli process to learn a set of recurring visual patterns, called ...
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Journal ArticleJournal of electrocardiology · January 2015
In this report we provide a method for automated detection of J wave, defined as a notch or slur in the descending slope of the terminal positive wave of the QRS complex, using signal processing and functional data analysis techniques. Two different sets o ...
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Journal ArticleAnat Rec (Hoboken) · January 2015
Three-dimensional geometric morphometric (3DGM) methods for placing landmarks on digitized bones have become increasingly sophisticated in the last 20 years, including greater degrees of automation. One aspect shared by all 3DGM methods is that the researc ...
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Journal ArticleIEEE transactions on bio-medical engineering · March 2014
Oscillatory phenomena abound in many types of signals. Identifying the individual oscillatory components that constitute an observed biological signal leads to profound understanding about the biological system. The instantaneous frequency (IF), the amplit ...
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Conference2014 IEEE International Conference on Image Processing, ICIP 2014 · January 28, 2014
We introduce an algorithm that removes the deleterious effect of cradling on X-ray images of paintings on wooden panels. The algorithm consists of a three stage procedure. Firstly, the cradled regions are located automatically. The second step consists of ...
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Journal Article2013 18th International Conference on Digital Signal Processing, DSP 2013 · December 6, 2013
The preservation of our cultural heritage is of paramount importance. Thanks to recent developments in digital acquisition techniques, powerful image analysis algorithms are developed which can be useful non-invasive tools to assist in the restoration and ...
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Journal ArticleJournal of Geophysical Research: Planets · September 1, 2013
We present a realistic application of an inversion scheme for global seismic tomography that uses as prior information the sparsity of a solution, defined as having few nonzero coefficients under the action of a linear transformation. In this paper, the sp ...
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Journal ArticleSignal Processing · March 1, 2013
This paper describes our methods for repairing and restoring images of hidden paintings (paintings that have been painted over and are now covered by a new surface painting) that have been obtained via noninvasive X-ray fluorescence imaging of their canvas ...
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Journal ArticleSignal Processing · March 1, 2013
Digital image processing is proving to be of great help in the analysis and documentation of our vast cultural heritage. In this paper, we present a new method for the virtual restoration of digitized paintings with special attention for the Ghent Altarpie ...
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Journal ArticleMathematics of Computation · January 17, 2013
This paper is a companion paper to [Yaron Lipman and Ingrid Daubechies, Conformal Wasserstein distances: Comparing surfaces in polynomial time, Adv. in Math. (ELS), 227 (2011), no. 3, 1047-1077, (2011)]. We provide numerical procedures and algorithms for c ...
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Journal Article2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings · January 1, 2013
In this paper, computer-based techniques for stylistic analysis of paintings are applied to the five panels of the 14th century Peruzzi Altarpiece by Giotto di Bondone. Features are extracted by combining a dual-tree complex wavelet transform with a hidden ...
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Journal ArticleLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) · November 30, 2012
Recent theoretical and experimental work in imaging neuroscience reveals that activations inferred from functional MRI data have sparse structure. We view sparse representation as a problem in Bayesian inference, following a machine learning approach, and ...
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Journal ArticleConstructive Approximation · April 1, 2012
Constructing a good approximation to a function of many variables suffers from the "curse of dimensionality". Namely, functions on ℝ N with smoothness of order s can in general be captured with accuracy at most O(n -s/N) using linear spaces or nonlinear ma ...
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Journal ArticleEuropean Signal Processing Conference · December 1, 2011
This paper describes our work on the problem of reconstructing the original visual appearance of underpaintings (paintings that have been painted over and are now covered by a new surface painting) from noninvasive X-ray fluorescence imaging data of their ...
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Journal ArticleProceedings - International Conference on Image Processing, ICIP · December 1, 2011
Objective characterization of jewels in paintings, especially pearls, has been a long lasting challenge for art historians. The way an artist painted pearls reflects his ability to observing nature and his knowledge of contemporary optical theory. Moreover ...
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Journal ArticleProceedings of SPIE - The International Society for Optical Engineering · November 2, 2011
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spheri ...
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Journal ArticleGeophysical Journal International · November 1, 2011
We propose a class of spherical wavelet bases for the analysis of geophysical models and for the tomographic inversion of global seismic data. Its multiresolution character allows for modelling with an effective spatial resolution that varies with position ...
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Journal ArticleLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) · September 2, 2011
In this paper, we present a new method for virtual restoration of digitized paintings, with the special focus on the Ghent Altarpiece (1432), one of Belgium's greatest masterpieces. The goal of the work is to remove cracks from the digitized painting there ...
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Journal ArticleICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings · August 18, 2011
This paper relates the style of 16th century Flemish paintings by Goossen van der Weyden (GvdW) to the style of preliminary sketches or underpaintings made prior to executing the painting. Van der Weyden made underpaintings in markedly different styles for ...
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Journal ArticleAdvances in Mathematics · June 20, 2011
We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation pro ...
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Journal ArticleAmerican journal of physical anthropology · June 2011
Inferred dietary preference is a major component of paleoecologies of extinct primates. Molar occlusal shape correlates with diet in living mammals, so teeth are a potentially useful structure from which to reconstruct diet in extinct taxa. We assess the e ...
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Journal ArticleAdvances in Adaptive Data Analysis · April 1, 2011
The synchrosqueezed transform was proposed recently in [Daubechies et al. (2009)] as an alternative to the empirical mode decomposition (EMD) [Huang et al. (1998)], to decompose composite signals into a sum of "modes" that each have well-defined instantane ...
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Journal ArticleProceedings of the International Congress of Mathematicians 2010, ICM 2010 · December 1, 2010
Yves Meyer has made numerous contributions to mathematics, several of which will be reviewed here, in particular in number theory, harmonic analysis and partial differential equations. His work in harmonic analysis led him naturally to take an interest in ...
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Journal ArticleIEEE Transactions on Information Theory · October 1, 2010
This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with ...
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Journal ArticleACM SIGGRAPH 2010 Papers, SIGGRAPH 2010 · July 26, 2010
We introduce the Symmetry Factored Embedding (SFE) and the Symmetry Factored Distance (SFD) as new tools to analyze and represent symmetries in a point set. The SFE provides new coordinates in which symmetry is "factored out," and the SFD is the Euclidean ...
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Journal ArticleJournal of Computational Physics · February 1, 2010
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, ℓ2 penalties are compared to so-called sparsity promoting ℓ1 and ℓ0 penalties, and a total variation penalty. Which of ...
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Journal ArticleNature communications · January 2010
Whether all the infectious herpesvirus particles entering a cell are able to replicate and/or express their genomes is not known. Here, we developed a general method to determine the number of viral genomes expressed in an infected cell. We constructed and ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 2010
Under certain conditions (known as the restricted isometry property, or RIP) on the m × N matrix Φ (wherem < N), vectors x ∈ R{double-struck}N that are sparse (i.e., have most of their entries equal to 0) can be recovered exactly from y:= Φx even though Φ- ...
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Journal ArticleEuropean Signal Processing Conference · December 1, 2009
Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis ...
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Journal ArticleProceedings of the National Academy of Sciences of the United States of America · July 2009
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the abso ...
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Journal ArticleProceedings of the National Academy of Sciences of the United States of America · June 2009
InfoMax and FastICA are the independent component analysis algorithms most used and apparently most effective for brain fMRI. We show that this is linked to their ability to handle effectively sparse components rather than independent components as such. T ...
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Journal Article · January 10, 2009
In a Hilbert space {Hilbert space}, discrete families of vectors {hj} with the property that f = ΣJ hJ for every f in {Hilbert space} are considered. This expansion formula is obviously true if the family is an orthonorma1 basis of {Hilbert space}, ...
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Journal Article · January 10, 2009
Two different procedures are studied by which a rrequency analysis of a time-dependenl signal can be effected, locally in lime. The lirst procedure is the short-time or windowed Fourier transform, the second is the "wavelet transform," in which high freque ...
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ConferenceDagstuhl Seminar Proceedings · January 1, 2009
New emerging technologies such as high-precision sensors or new MRI machines drive us towards a challenging quest for new, more effective, and more daring mathematical models and algorithms. Therefore, in the last few years researchers have started to inve ...
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Journal ArticleProceedings - International Conference on Image Processing, ICIP · January 1, 2009
This paper examines whether machine learning and image analysis tools can be used to assist art experts in the authentication of unknown or disputed paintings. Recent work on this topic [1] has presented some promising initial results. Our reexamination of ...
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Journal ArticleJournal of Fourier Analysis and Applications · December 1, 2008
Regularization of ill-posed linear inverse problems via ℓ1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an ℓ1 penalized functional is via an iterative soft-thresholding ...
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Journal ArticleCISS 2008, The 42nd Annual Conference on Information Sciences and Systems · September 24, 2008
Given an m × N matrix Φ, with m < N, the system of equations Φx = y is typically underdetermined and has infinitely many solutions. Various forms of optimization can extract a "best" solution. One of the oldest is to select the one with minimal l2 norm. It ...
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Journal ArticleIEEE Signal Processing Magazine · January 1, 2008
A description on the approaches to brushwork analysis and artist identification within the framework of data set is given. Image processing is now a reality in painting analysis as high resolution and richer data are also available. A summary on the result ...
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Journal ArticleAdvances in Imaging and Electron Physics · January 1, 2008
Several iterative strategies for solving inverse problems in the context of signal and image processing are discussed. Problems for which it is reasonable to assume that the solution has a sparse expansion with respect to a wavelet basis or frame are focus ...
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Journal ArticleAnnals of Statistics · December 1, 2007
We introduce a useful tool for analyzing boosting algorithms called the "smooth margin function," a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin, "coordinate ascent ...
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Journal ArticleIEEE Transactions on Information Theory · November 1, 2007
A scheme for simple oversampled analog-to-digital (A/D) conversion using single-bit quantization is presented. The scheme is based on recording positions of zero-crossings of the input signal added to a deterministic dither function. This information can b ...
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Journal ArticleMultiscale Modeling and Simulation · August 1, 2007
We develop a new sparse spectral method, in which the fast Fourier transform (FFT) is replaced by RAℓSFA (randomized algorithm of sparse Fourier analysis); this is a sublinear randomized algorithm that takes time O(B log N) to recover a B-term Fourier repr ...
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Journal ArticleGeophysical Journal International · July 1, 2007
We propose the use of ℓ1 regularization in a wavelet basis for the solution of linearized seismic tomography problems Am = d, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used t ...
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Journal ArticleInverse Problems and Imaging · January 1, 2007
We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of thi ...
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Journal ArticleProceedings - International Conference on Image Processing, ICIP · December 1, 2006
Mutual information (MI) based methods for image registration enjoy great experimental success and are becoming widely used. However, they impose a large computational burden that limits their use; many applications would benefit from a reduction of the com ...
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Journal ArticleIEEE Transactions on Information Theory · August 1, 2006
Beta-encoders with error correction were introduced by Daubechies, DeVore, Güntürk and Vaishampayan as an alternative to pulse-code modulation (PCM) for analog-to-digital conversion. An N -bit beta-encoder quantizes a real number by computing one of its N- ...
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Journal ArticleIEEE Transactions on Information Theory · March 1, 2006
This paper analyzes mathematically the effect of quantizer threshold imperfection commonly encountered in the circuit implementation of analog-to-digltal (A/D) converters such as pulse code modulation (PCM) and sigma-delta (∑Δ) modulation. ∑Δ modulation, w ...
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Journal ArticleJournal of Computational Physics · January 20, 2006
We analyze a sublinear RAℓSFA (randomized algorithm for Sparse Fourier analysis) that finds a near-optimal B-term Sparse representation R for a given discrete signal S of length N, in time and space poly (B, log(N)), following the approach given in [A.C. G ...
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Journal ArticleAIP Conference Proceedings · November 23, 2005
In an exploratory approach to data analysis, it is often useful to consider the observations as generated from a set of latent generators or "sources" via a generally unknown mapping. For the noisy overcomplete case, where we have more sources than observa ...
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Journal ArticleApplied and Computational Harmonic Analysis · July 1, 2005
Inspired by papers of Vese-Osher [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and Osher-Solé-Vese [Image decomposition and restoration using total variation minimization an ...
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Journal ArticleMonthly Notices of the Royal Astronomical Society · May 1, 2005
We present a new method for component separation aimed at extracting Sunyaev-Zel'dovich (SZ) galaxy clusters from multifrequency maps of cosmic microwave background (CMB) experiments. This method is designed to recover non-Gaussian, spatially localized and ...
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Journal Article · January 1, 2005
As an approximation to a relativistic one-electron molecule, we study the operator H=(-Δ+m2)1/2-e2 Z j|x-Rj|-1 with Zj0, e -2=137.04. H is bounded below if and only if e2 Z j>2/π, all j. Assuming this condition, the system is unstable when e2ΣZj>2/π in the ...
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Journal ArticleInternet Mathematics · January 1, 2005
The connectivity of the autonomous systems (ASs) in the Internet can be modeled as a time-evolving random graph, whose nodes represent ASs and whose edges represent direct connections between them. Even though this graph has some random aspects, its proper ...
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Journal ArticleJournal of Machine Learning Research · December 1, 2004
In order to study the convergence properties of the AdaBoost algorithm, we reduce AdaBoost to a nonlinear iterated map and study the evolution of its weight vectors. This dynamical systems approach allows us to understand AdaBoost's convergence properties ...
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Journal ArticleCommunications on Pure and Applied Mathematics · November 1, 2004
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted of ℓP - penalties on the coefficients ...
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Journal ArticleProceedings of SPIE - The International Society for Optical Engineering · May 10, 2004
We discuss a wavelet based treatment of variational problems arising in the context of image processing, inspired by papers of Vese-Osher and Osher-Solé-Vese, in particular, we introduce a special class of variational functionals, that induce a decompositi ...
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Journal ArticleConstructive Approximation · January 1, 2004
A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study properties such as regularity, convergence, and stability of a normal mult ...
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Journal ArticleLecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) · January 1, 2004
We study two boosting algorithms, Coordinate Ascent Boosting and Approximate Coordinate Ascent Boosting, which are explicitly designed to produce maximum margins. To derive these algorithms, we introduce a smooth approximation of the margin that one can ma ...
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Journal ArticleConstructive Approximation · January 1, 2004
Starting from any two compactly supported refutable functions in L 2 (R) with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2 (R). Mo ...
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ConferenceAdvances in Neural Information Processing Systems · January 1, 2004
In order to understand AdaBoost's dynamics, especially its ability to maximize margins, we derive an associated simplified nonlinear iterated map and analyze its behavior in low-dimensional cases. We find stable cycles for these cases, which can explicitly ...
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Journal ArticleRevista Matematica Iberoamericana · January 1, 2003
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is "almost" characterized by wavelet expansions in the following sense: if a function f is i ...
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Journal ArticleApplied and Computational Harmonic Analysis · January 1, 2003
We discuss wavelet frames constructed via multiresolution analysis (MRA), with emphasis on tight wavelet frames. In particular, we establish general principles and specific algorithms for constructing framelets and tight framelets, and we show how they can ...
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Journal ArticleIEEE Transactions on Information Theory · July 1, 2002
This paper provides a mathematical analysis of transform compression in its relationship to linear and nonlinear approximation theory. Contrasting linear and nonlinear approximation spaces, we show that there are interesting classes of functions/random pro ...
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Journal ArticleIEEE Transactions on Information Theory · June 1, 2002
The concept of democracy was introduced in which the individual bits in a coarsely quantized representation of a signal were given equal weight in the approximation to the original signal. It was proved that such democratic representations could not achiev ...
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ConferenceData Compression Conference Proceedings · January 1, 2002
The problem of reconstructing a π-bandlimited signal f from its quantized samples taken at an irregular sequence of points (tk)k∈ZZ arises in oversampled analog-to-digital conversion. The input signal can be reconstructed from the quantized samples (f(tk)) ...
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Journal ArticleProceedings - IEEE International Symposium on Circuits and Systems · January 1, 2002
We introduce a new architecture for pipelined (and also algorithmic) A/D converters that give exponentially accurate conversion using inaccurate comparators. An error analysis of a sigma-delta converter with an imperfect comparator and a constant input rev ...
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Journal ArticleConstructive Approximation · December 1, 2001
We present a generalization of the commutation formula to irregular subdivision schemes and wavelets. We show how, in the noninterpolating case, the divided differences need to be adapted to the subdivision scheme. As an example we include the construction ...
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Journal ArticleApplied and Computational Harmonic Analysis · September 1, 2001
Tree approximation is a new form of nonlinear approximation which appears naturally in some applications such as image processing and adaptive numerical methods. It is somewhat more restrictive than the usual n-term approximation. We show that the restrict ...
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Journal ArticleIEEE Transactions on Information Theory · December 1, 2000
In this paper the windowed Fourier encoding-decoding scheme applied to the multiple description compression problem is analyzed. In the general case, four window functions are needed to define the encoder and decoder, although this number can be reduced to ...
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Journal ArticleData Compression Conference Proceedings · January 1, 2000
We present a scheme for simple oversampled analog-to-digital conversion, with single bit quantization and exponential error decay in the bit-rate. The scheme is based on recording positions of zero-crossings of the input signal added to a deterministic dit ...
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Journal ArticleConstructive Approximation · January 1, 1999
We study the smoothness of the limit function for one-dimensional unequally spaced interpolating subdivision schemes. The new grid points introduced at every level can lie in irregularly spaced locations between old, adjacent grid points and not only midwa ...
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Journal ArticlePhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · January 1, 1999
In this article we review techniques for building and analysing wavelets on irregular point sets in one and two dimensions. We discuss current results on both the practical and theoretical sides. In particular, we focus on subdivision schemes and commutati ...
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Journal ArticleIEEE Transactions on Information Theory · December 1, 1998
In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon's R(D) theory in the case of Gaussian stationary processes, which says that transforming into a Fourier basis followed ...
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ConferenceProceedings of SPIE - The International Society for Optical Engineering · March 26, 1998
We present three recent developments in wavelets and subdivision: wavelet-type transforms that map integers to integers, with an application to lossless coding for images; rate-distortion bounds that realize the compression given by nonlinear approximation ...
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Journal ArticleApplied and Computational Harmonic Analysis · January 1, 1998
Invertible wavelet transforms that map integers to integers have important applications in lossless coding. In this paper we present two approaches to build integer to integer wavelet transforms. The first approach is to adapt the precoder of Laroia et al. ...
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Journal ArticleJournal of Electronic Imaging · January 1, 1998
We present three recent developments in wavelets and subdivision: wavelet-type transforms that map integers to integers, with an application to lossless coding for images; rate-distortion bounds that realize the compression given by nonlinear approximation ...
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Journal ArticleJournal of Fourier Analysis and Applications · January 1, 1998
This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also k ...
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Journal ArticleIEEE International Conference on Image Processing · December 1, 1997
Invertible wavelet transforms that map integers to integers are important for lossless representations. In this paper, we present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting st ...
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Journal ArticleIEEE Signal Processing Letters · December 1, 1997
A geometrical description is given for reassignment vector fields of spectrograms. These vector fields are shown to be connected with both an intrinsic phase characterization and a scalar potential. This allows for the generalization of the original reassi ...
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Journal ArticleIEEE Transactions on Signal Processing · December 1, 1997
There are many signal processing tasks for which convolution-based continuous signal representations such as splines and wavelets provide an interesting and practical alternative to the more traditional sine-based methods. The coefficients of the correspon ...
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Journal ArticleJournal of Fourier Analysis and Applications · January 1, 1997
We study the existence and regularity of compactly supported solutions φ = (φν)ν=0r- 1 of vector refinement equations. The space spanned by the translates of φν can only provide approximation order if the refinement mask P has certain particular factorizat ...
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Journal ArticleProceedings of the IEEE · April 1, 1996
The subject area of wavelets is connected to older ideas in many other fields, including pure and applied mathematics, physics, computer science and engineering. The rapid development of wavelet tools led to the application of wavelets as a standard part o ...
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Journal ArticleRevista Matematica Iberoamericana · January 1, 1996
We study the regularity of refinable functions by analyzing the spectral properties of special operators associated to the refinement equation; in particular, we use the Fredholm determinant theory to derive numerical estimates for the spectral radius of t ...
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Journal ArticleConstructive Approximation · September 1, 1995
If the mask of a refinable function has infinitely many coefficients, or if the coefficients are irrational, then it is often replaced by a finite mask with coefficients with terminating decimal expansions when it comes to applications. This note studies h ...
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Journal ArticleJournal of Fourier Analysis and Applications · January 1, 1994
Gabor time-frequency lattices are sets of functions of the form (Formula presented.) generated from a given function (Formula presented.) by discrete translations in time and frequency. They are potential tools for the decomposition and handling of signals ...
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Journal ArticleWavelet Analysis and Its Applications · January 1, 1994
The following two questions are often asked by researchers interested in applying wavelet bases to concrete numerical problems: 1) how does one adapt a wavelet basis on IR to a wavelet basis on an interval without terrible edge effects? 2) how does the wav ...
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Journal ArticleIEEE Transactions on Information Theory · January 1, 1993
It is shown that there is a trade-off between the smoothness and decay properties of the dual functions, occurring in the lattice expansion problem. More precisely, it is shown that if g and [formula Omitted] are dual, then 1) at least one of H1/2
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Journal ArticleLinear Algebra and Its Applications · January 15, 1992
An infinite product ∏∞i=1Mi of matrices converges (on the right) if limi→∞ M1 ... Mi exists. A set ∑={Ai:i≥1}of n x n matrices is called an RCP set (right- convergent product set) if all infinite products with each element drawn from ∑ converge. Such sets ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1992
Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with ...
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ConferenceICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings · January 1, 1992
A combination of trellis coded quantization (TCQ) and its vector alphabet generalization TCVQ is used to code the coefficients resulting from a biorthogonal wavelet transform in an image. TCVQ is a vector trellis coder with fixed rate, very good rate-disto ...
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Journal ArticleIEEE transactions on image processing : a publication of the IEEE Signal Processing Society · January 1992
A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: ...
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Journal ArticleICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings · December 1, 1990
A two-step scheme for image compression that takes into account psychovisual features in space and frequency domains is proposed. A wavelet transform is first used in order to obtain a set of orthonormal subclasses of images; the original image is decompos ...
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Journal ArticleIEEE Transactions on Information Theory · January 1, 1990
Two different procedures are studied by which a frequency analysis of a time-dependent signal can be effected, locally in time. The first procedure is the short-time or windowed Fourier transform, the second is the “wavelet transform,” in which high freque ...
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Journal Article · December 1, 1989
Summary form only given. In the simplest case, a family wavelets is generated by dilating and translating a single function of one variable: ha,b(x) = |a|-1/2h (x-b/a). The parameters a and b may vary continuously, or be restricted to a discrete lattice of ...
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Journal Article · December 1, 1988
Summary form only given, as follows. Two different procedures are studied by which a frequency analysis of a time-dependent signal can be effected, locally in time. The first procedure is the short-time or windowed Fourier transform; the second is the wave ...
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Journal ArticleInverse Problems · December 1, 1988
Operators which localise both in time and frequency are constructed. They restrict to a finite time interval and cut off low as well as high frequencies (band-pass filters). Explicit expressions for eigenvalues and eigenfunctions (Laguerre functions) are g ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1988
We look at the decomposition of arbitrary f in L2(R) in terms of the family of functions φmn(x) = π−1/4exp{ − 1/2imnab + i max − 1/2(x − nb)2}, with a, b > 0. We derive bounds and explicit formulas for the minimal expansion coefficients in the case where a ...
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Journal ArticleCommunications on Pure and Applied Mathematics · January 1, 1988
We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms ...
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Journal ArticleIEEE Transactions on Information Theory · January 1, 1988
We define a set of operators which localize in both time and frequency. These operators are similar to but different from the low-pass time-limiting operators, the singular functions of which are the prolate spheroidal wave functions. Our construction diff ...
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Journal ArticleJournal of Mathematical Physics · January 1, 1987
The results obtained earlier have been generalized to show that the path integral for the affine coherent state matrix element of a unitary evolution operator exp(-iTH) can be written as a well-defined Wiener integral, involving Wiener measure on the Lobac ...
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Journal ArticleJournal of Mathematical Physics · January 1, 1986
In a Hilbert spaced ℋ, discrete families of vectors {hj} with the property that f = ∑j〈j|f〉h j for every f in ℋ are considered. This expansion formula is obviously true if the family is an orthonormal basis of ℋ, but also can hold in situations where the h ...
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Journal ArticleJournal of Mathematical Physics · January 1, 1985
The coherent-state representation of quantum-mechanical propagators as well-defined phase-space path integrals involving Wiener measure on continuous phase-space paths in the limit that the diffusion constant diverges is formulated and proved. This constru ...
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Journal ArticleCommunications in Mathematical Physics · December 1, 1984
We discuss the discrete spectrum of the operator {Mathematical expression}. More specifically, we study 1) the behaviour of the eigenvalues when the internuclear distances contract, 2) the existence of a c-independent lower bound for HK(c)-mc2, 3) the nonr ...
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Journal ArticleNorth-Holland Mathematics Studies · January 1, 1984
As an approximation to a relativistic one-electron molecule, we study the operator, with Zj≥ 0 for all j. H is bounded below iff for all j. Under this condition, we show that 1) The system is stable when the nuclear repulsion is taken into account, i.e., w ...
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Journal ArticlePhysical Review Letters · January 1, 1984
We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well defined path integrals involving Wiener ...
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Journal ArticleCommunications in Mathematical Physics · December 1, 1983
As an approximation to a relativistic one-electron molecule, we study the operator {Mathematical expression} with Zj≧0, e-2=137.04. H is bounded below if and only if e2Zj≦2/π all j. Assuming this condition, the system is unstable when e2∑Zj>2/π in the sens ...
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Journal ArticleCommunications in Mathematical Physics · December 1, 1983
We derive semiclassical upper bounds for the number of bound states and the sum of negative eigenvalues of the one-particle Hamiltonians h=f(-i∇)+V(x) acting on L2(ℝn). These bounds are then used to derive a lower bound on the kinetic energy {Mathematical ...
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Journal ArticleLetters in Mathematical Physics · May 1, 1983
We show that the coherent state matrix elements of the quantum mechanical propagator for all quadratic Hamiltonians may be represented as the limit of path integrals with respect to appropriately modified Wiener measures as the associated diffusion constan ...
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Journal ArticlePhysical Review Letters · January 1, 1982
By exploitation of the overcompleteness of coherent states expressions are presented for path integrals in terms of genuine (Wiener) path-space measures for driven harmonic oscillators which when projected onto the subspace spanned by coherent-state matrix ...
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Journal ArticleJournal of Mathematical Physics · January 1, 1982
We study in more detail the mathematical properties of the integral transform relating the matrix elements between coherent states of a quantum operator to the corresponding classical function. Explicit families of Hilbert spaces are constructed between wh ...
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Journal ArticleJournal of Mathematical Physics · January 1, 1982
We use the properties of an integral transform relating a classical function f with the matrix elements between coherent states of its quantal counterpart Q f, to derive continuity properties of the Weyl transform from classes of distributions to classes o ...
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Journal ArticleJournal of Mathematical Physics · January 1, 1981
The overcompleteness of the coherent states for the Heisenberg-Weyl group implies that many different integral kernels can be used to represent the same operator. Within such an equivalence class we construct an integral kernel to represent the quantum-mec ...
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Journal ArticleCommunications in Mathematical Physics · October 1, 1980
Using properties of an integral transform giving directly the matrix elements of a quantum mechanical operator from the corresponding classical function, we restrict the class of distributions corresponding to bounded operators. As a consequence, we can ex ...
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Journal ArticleJournal of Mathematical Physics · January 1, 1979
We study in some detail the correspondence between a function f on phase space and the matrix elements (Qf)(a, b) of its quantized Q f between the coherent states |a< and |b<. It is an integral transform: Qf(a, b) = ∫{a, b |v} f(v) dv which resembles in ma ...
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Journal ArticleLetters in Mathematical Physics · January 1, 1979
We display three equivalent conditions for a sublattice, isomorphic to a P {Mathematical expression}, of the propositional system P(ℋ) of a quantum system to be the representation of a physical subsystem (see [1]). These conditions are valid for dim {Mathe ...
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Journal ArticleLetters in Mathematical Physics · January 1, 1979
Working within the framework of the propositional system formalism, we use a previous study [1] of the description of two independent physical systems as one big physical system to derive a characterization of a (non-interacting) physical subsystem. We dis ...
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Journal ArticleLetters in Mathematical Physics · November 1, 1978
We use a hyperdifferential operator approach to study holomorphic quantization. We explicitly construct the Hilbert space operator which corresponds to a given holomorphic function. We further construct the adjoint and products of such operators and we dis ...
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