Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets

This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering such sets through compressive measurements, while simultaneously providing adaptive support recovery protocols that perform near optimally for these classes. We show that by adaptively designing the sensing matrix we can attain significant performance gains over non-adaptive protocols. These gains arise from the fact that adaptive sensing can: (i) better mitigate the effects of noise, and (ii) better capitalize on the structure of the support sets.Comment: to appear in IEEE Transactions on Information Theor

Lower bounds for sparse recovery problems

Sparse recovery or compressed sensing is the problem of estimating a signal from noisy linear measurements of that signal. Sparse recovery has traditionally been used in areas like image acquisition, streaming algorithms, genetic testing, and, more recently, for image recovery tasks. Over the last decade many techniques have been developed for sparse recovery under various guarantees. We develop new lower bound techniques and show the tightness of existing results for the following variants of the sparse recovery problem: (i) adaptive sparse recovery, (ii) sparse recovery under high SNR, (iii) deterministic L2 heavy hitters, and, (iv) compressed sensing with generative models.Computer Science