Info-Greedy sequential adaptive compressed sensing
This work addresses the challenge of efficient signal acquisition in compressed sensing for applications like imaging or sensing, offering an incremental improvement over existing methods.
The paper tackles the problem of sequential adaptive compressed sensing by proposing Info-Greedy Sensing, a framework that selects measurements to maximize information gain, and demonstrates that it significantly outperforms random projection for signals with sparse and low-rank covariance matrices, with adaptivity providing robustness against distribution mismatches.
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.