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Bayesian compressive sensing

Publication ,  Journal Article
Ji, S; Xue, Y; Carin, L
Published in: IEEE Transactions on Signal Processing
June 1, 2008

The data of interest are assumed to be represented as N-dimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basis-function coefficients associated with B. Compressive sensing is a framework whereby one does not measure one of the aforementioned N-dimensional signals directly, but rather a set of related measurements, with the new measurements a linear combination of the original underlying N-dimensional signal. The number of required compressive-sensing measurements is typically much smaller than N, offering the potential to simplify the sensing system. Let f denote the unknown underlying N-dimensional signal, and g a vector of compressive-sensing measurements, then one may approximate f accurately by utilizing knowledge of the (under-determined) linear relationship between f and g, in addition to knowledge of the fact that f is compressible in B. In this paper we employ a Bayesian formalism for estimating the underlying signal f based on compressive-sensing measurements g. The proposed framework has the following properties: i) in addition to estimating the underlying signal f, "error bars"are also estimated, these giving a measure of confidence in the inverted signal; ii) using knowledge of the error bars, a principled means is provided for determining when a sufficient number of compressive-sensing measurements have been performed; iii) this setting lends itself naturally to a framework whereby the compressive sensing measurements are optimized adaptively and hence not determined randomly; and iv) the framework accounts for additive noise in the compressive-sensing measurements and provides an estimate of the noise variance. In this paper we present the underlying theory, an associated algorithm, example results, and provide comparisons to other compressive-sensing inversion algorithms in the literature. © 2008 IEEE.

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Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

June 1, 2008

Volume

56

Issue

6

Start / End Page

2346 / 2356

Related Subject Headings

  • Networking & Telecommunications
 

Citation

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Ji, S., Xue, Y., & Carin, L. (2008). Bayesian compressive sensing. IEEE Transactions on Signal Processing, 56(6), 2346–2356. https://doi.org/10.1109/TSP.2007.914345
Ji, S., Y. Xue, and L. Carin. “Bayesian compressive sensing.” IEEE Transactions on Signal Processing 56, no. 6 (June 1, 2008): 2346–56. https://doi.org/10.1109/TSP.2007.914345.
Ji S, Xue Y, Carin L. Bayesian compressive sensing. IEEE Transactions on Signal Processing. 2008 Jun 1;56(6):2346–56.
Ji, S., et al. “Bayesian compressive sensing.” IEEE Transactions on Signal Processing, vol. 56, no. 6, June 2008, pp. 2346–56. Scopus, doi:10.1109/TSP.2007.914345.
Ji S, Xue Y, Carin L. Bayesian compressive sensing. IEEE Transactions on Signal Processing. 2008 Jun 1;56(6):2346–2356.

Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

June 1, 2008

Volume

56

Issue

6

Start / End Page

2346 / 2356

Related Subject Headings

  • Networking & Telecommunications