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arXiv · 1407.0731

Info-Greedy sequential adaptive compressed sensing

Gabor Braun·Sebastian Pokutta·Yao Xie
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Abstract

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.

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BibTeXRIS

Gabor Braun, Sebastian Pokutta, Yao Xie. 2014-07-02. Info-Greedy sequential adaptive compressed sensing. https://doi.org/10.1109/jstsp.2015.2400428

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