Info-Greedy sequential adaptive compressed sensing

TL;DR

This paper introduces an information-theoretic framework for sequential adaptive compressed sensing, called Info-Greedy Sensing, which optimizes measurements to maximize information gain and improves performance over traditional methods.

Contribution

It develops an Info-Greedy approach for adaptive sensing, connecting it with blackbox complexity, and provides algorithms for sparse, Gaussian, and GMM signals with demonstrated effectiveness.

Findings

Significant performance improvements over random projections.

Robustness to distribution mismatches.

Effective algorithms for sparse and GMM signals.

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.