Average case analysis of multichannel sparse recovery using convex relaxation

This paper considers recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given observations, including thresholding, simultaneous orthogonal matching pursuit (SOMP), and convex relaxation based on a mixed matrix norm. Typically, worst case analysis is carried out in order to analyze conditions under which the algorithms are able to recover any jointly sparse set of vectors. However, such an approach is not able to provide insights into why joint sparse recovery is superior to applying standard sparse reconstruction methods to each channel individually. Previous work considered an average case analysis of thresholding and SOMP by imposing a probability model on the measured signals. Here, the main focus is on analysis of convex relaxation techniques. In particular, the mixed `2;1 approach to multichannel recovery is investigated. Under a very mild condition on the sparsity and...

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: Yonina C. Eldar, Holger Rauhut
• Keywords: Convex Relaxation, Convex Relaxation Technique, Education, Sparse, TIT 2010