Enhanced joint sparsity via Iterative Support Detection

Compressed sensing (CS) [1, 2] demonstrates that sparse signals can be recovered from underdetermined linear measurements. The idea of iterative support detection (ISD, for short) method first proposed by Wang et. al [3] has demonstrated its superior performance for the reconstruction of the single channel sparse signals. In this paper, we extend ISD from sparsity to the more general structured sparsity, by considering a specific case, i.e. joint sparsity based recovery problem where multiple signals share the same common sparse support sets, and they are measured through the same sensing matrix. While ISD can be applied to various existing models and algorithms of joint sparse recovery, we consider the popular l2,1 convex model. Numerical tests show that ISD brings significant recovery enhancement for the plain l2,1 model, and performs even better than the simultaneous orthogonal matching pursuit (SOMP) algorithm and p-threshold algorithm in both noiseless and noisy environments in our settings. More important, the original ISD paper shows that ISD fails to bring benefits for the plain l1 model for the single channel sparse Bernoulli signals, where the nonzero components has the same amplitude, because the fast decaying property of the nonzeros is required for the performance improvement when threshold based support detection is adopted. However, as for the joint sparsity, we have found that ISD is still able to bring significant recovery improvement, even for the multichannel sparse Bernoulli signals, partially because the joint sparsity structure can be naturally incorporated into the implementation of ISD and we will give some preliminary analysis on it. ∗Corresponding author Email address: [email protected] (Yilun Wang ) Preprint submitted to Elsevier December 25, 2014