Signal Recovery in Compressive Sensing via Multiple Sparsifying Bases

U. L. Wijewardhana, Evgeny Belyaev, M. Codreanu, M. Latva-Aho

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Compressive sensing theory asserts that, under certain conditions, a high dimensional but compressible signal can be recovered from a small number of random linear projections by utilizing computationally efficient algorithms. The a priori knowledge of the basis in which the signal of interest is sparse is the key assumption utilized by such algorithms. However, the basis in which the signal is the sparsest is unknown for many natural signals of interest. Instead there may exist multiple bases which lead to a compressible representation of the signal: e.g., an image is compressible in different wavelet transforms. We show that a significant performance improvement can be achieved by utilizing multiple estimates of the signal using sparsifying bases in the context of signal reconstruction from compressive samples. Further, we derive a customized interior-point method to jointly obtain multiple estimates of a 2-D signal (image) from compressive measurements utilizing multiple sparsifying bases as well as the fact that the images usually have a sparse gradient.
Original languageEnglish
Title of host publicationProceedings of 2017 Data Compression Conference
Volume127767
PublisherIEEE
Publication date2017
Pages141-150
Article number7921909
ISBN (Print)9781509067213
DOIs
Publication statusPublished - 2017
Event2017 Data Compression Conference - Snowbird, United States
Duration: 4 Apr 20177 Apr 2017

Conference

Conference2017 Data Compression Conference
CountryUnited States
CitySnowbird
Period04/04/201707/04/2017
SeriesData Compression Conference. Proceedings
ISSN1068-0314

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