Variational Bayesian Compressed Sensing for Sparse and Locally Constant Signals

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we deal with the signal recovery problem in compressed sensing, that is, the problem of estimating the original signal from its linear measurements. Recovery algorithms can be mainly classified into two types, optimization based algorithms and statistical modeling based algorithms. Basis pursuit (BP) or basis pursuit denoising (BPDN) is one of the most widely used optimization based recovery algorithms, that minimizes the \ell-{1} norm of the signal or its coefficients in some basis under the constraint that its linear transform is equal to or close to the observation signal. There are various extensions of those algorithms depending on the problem structure. When the original signal is an image, the objective function is often the sum of the \ell-{1} norm of the coefficients of the signal in some basis and a total variation (TV) of the image. It can be considered that it requires the image to be sparse in both the specific transform domain and finite differences at the same time. In this paper, we propose a statistical model that represents those sparsities and the signal recovery algorithm based on the variational method. One of the advantages of the statistical approach is that we can utilize the posterior information of the original signal and it is known that it can be used to construct the compressed sensing measurements adaptively. The proposed recovery algorithm and adaptive construction of the compressed sensing measurements are validated on numerical experiments.

Original languageEnglish
Title of host publication2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages972-976
Number of pages5
ISBN (Electronic)9789881476852
DOIs
Publication statusPublished - 2019 Mar 4
Event10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Honolulu, United States
Duration: 2018 Nov 122018 Nov 15

Publication series

Name2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings

Conference

Conference10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018
CountryUnited States
CityHonolulu
Period18/11/1218/11/15

Fingerprint

Compressed sensing
Recovery

ASJC Scopus subject areas

  • Information Systems

Cite this

Horii, S. (2019). Variational Bayesian Compressed Sensing for Sparse and Locally Constant Signals. In 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings (pp. 972-976). [8659457] (2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/APSIPA.2018.8659457

Variational Bayesian Compressed Sensing for Sparse and Locally Constant Signals. / Horii, Shunsuke.

2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 972-976 8659457 (2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Horii, S 2019, Variational Bayesian Compressed Sensing for Sparse and Locally Constant Signals. in 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings., 8659457, 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 972-976, 10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018, Honolulu, United States, 18/11/12. https://doi.org/10.23919/APSIPA.2018.8659457
Horii S. Variational Bayesian Compressed Sensing for Sparse and Locally Constant Signals. In 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 972-976. 8659457. (2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings). https://doi.org/10.23919/APSIPA.2018.8659457
Horii, Shunsuke. / Variational Bayesian Compressed Sensing for Sparse and Locally Constant Signals. 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 972-976 (2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings).
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