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On some iterative concepts for image restoration

Publication ,  Journal Article
Daubechies, I; Teschke, G; Vese, L
Published in: Advances 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 focused. A variational formulation of the problem is considered and an iteration scheme for which the iterates approximate the solution is constructed. The concrete problem of simultaneously denoising, decomposing, and deblurring a given image, is discussed. The associated variational formulation of the problem contains terms that promote sparsity and smoothness. A natural extension to vector-valued inverse problems is also considered. In the linear case, and under fairly general assumptions on the constraint, its is proved that weak convergence of the iterative scheme always holds.

Duke Scholars

Published In

Advances in Imaging and Electron Physics

DOI

ISSN

1076-5670

Publication Date

January 1, 2008

Volume

150

Start / End Page

1 / 51

Related Subject Headings

  • Microscopy
 

Citation

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MLA
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Daubechies, I., Teschke, G., & Vese, L. (2008). On some iterative concepts for image restoration. Advances in Imaging and Electron Physics, 150, 1–51. https://doi.org/10.1016/S1076-5670(07)00001-8
Daubechies, I., G. Teschke, and L. Vese. “On some iterative concepts for image restoration.” Advances in Imaging and Electron Physics 150 (January 1, 2008): 1–51. https://doi.org/10.1016/S1076-5670(07)00001-8.
Daubechies I, Teschke G, Vese L. On some iterative concepts for image restoration. Advances in Imaging and Electron Physics. 2008 Jan 1;150:1–51.
Daubechies, I., et al. “On some iterative concepts for image restoration.” Advances in Imaging and Electron Physics, vol. 150, Jan. 2008, pp. 1–51. Scopus, doi:10.1016/S1076-5670(07)00001-8.
Daubechies I, Teschke G, Vese L. On some iterative concepts for image restoration. Advances in Imaging and Electron Physics. 2008 Jan 1;150:1–51.
Journal cover image

Published In

Advances in Imaging and Electron Physics

DOI

ISSN

1076-5670

Publication Date

January 1, 2008

Volume

150

Start / End Page

1 / 51

Related Subject Headings

  • Microscopy