Info-Greedy Sequential Adaptive Compressed Sensing

We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the widely used bisection approach is Info-Greedy for a family of...

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Bibliographic Details
Published inIEEE journal of selected topics in signal processing Vol. 9; no. 4; pp. 601 - 611
Main Authors Braun, Gabor, Pokutta, Sebastian, Yao Xie
Format Journal Article
LanguageEnglish
Published IEEE 01.06.2015
Subjects
adaptive estimation
adaptive signal detection
Compressed sensing
mutual information
Noise
Noise measurement
Power measurement
Sensors
Signal processing algorithms
Vectors
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ISSN1932-4553
1941-0484
DOI10.1109/JSTSP.2015.2400428

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Summary:We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the widely used bisection approach is Info-Greedy for a family of k-sparse signals by connecting compressed sensing and blackbox complexity of sequential query algorithms, and present Info-Greedy algorithms for Gaussian and Gaussian mixture model (GMM) signals, as well as ways to design sparse Info-Greedy measurements. Numerical examples demonstrate the good performance of the proposed algorithms using simulated and real data: Info-Greedy Sensing shows significant improvement over random projection for signals with sparse and low-rank covariance matrices, and adaptivity brings robustness when there is a mismatch between the assumed and the true distributions.
ISSN:1932-4553
1941-0484
DOI:10.1109/JSTSP.2015.2400428