A Sparse Recovery Algorithm Based on Ratio of Stable Variables with Small Alpha

In Compressed Sensing, recovery algorithms become poorer in efficiency when the problem dimension and signal sparsity increase. To reconstruct the large-scale sparse signal efficiently, a novel sparse recovery algorithm is proposed based on extremely heavy-tailed ratio of stable variables with small α. In the algorithm, the measurement matrix samples from a small α-stable distribution, which generates samples extremely close to the magnitude of each coordinate. Utilizing these samples, nonzero coordinates can be estimated exactly by a few iterations. Comparisons with BP algorithm and OMP algorithm demonstrate that the proposed algorithm could be faster in decoding speed, especially as the signal sparsity is not small. In addition, the reported experiments show that the recovery accuracy of our procedure is invariant for additional measurement noise.