Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

The theory of compressed sensing shows that sparsity pattern (or support) of a sparse signal can be recovered from a small number of appropriate linear projections (samples). Unfortunately, as soon as noise is added, the number of required samples exceeds the full signal dimension, rendering compressed sensing ineffective. In recent work, we have shown that this can be fixed if a small distorti...

Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML) frameworks and study the conditions for perfect reconstruction of the original row sparsity and row sparsity pattern. However, the confidence-constrained opt...

We study the problem of recovering the sparsity pattern of block-sparse signals from noise-corrupted measurements. A simple, efficient recovery method, namely, a block-version of the orthogonal matching pursuit (OMP) method, is considered in this paper and its behavior for recovering the block-sparsity pattern is analyzed. We provide sufficient conditions under which the block-version of the OM...

Sparsity Pattern Recovery in Compressed Sensing by Galen Reeves Doctor of Philosophy in Engineering — Electrical Engineering and Computer Sciences University of California, Berkeley Professor Michael Gastpar, Chair The problem of recovering sparse signals from a limited number of measurements is now ubiquitous in signal processing, statistics, and machine learning. A natural question of fundame...

In this paper, we consider the block-sparse signals recovery problem in the context of multiple measurement vectors (MMV) with common row sparsity patterns. We develop a new method for recovery of common row sparsity MMV signals, where a pattern-coupled hierarchical Gaussian prior model is introduced to characterize both the block-sparsity of the coefficients and the statistical dependency betw...