Abstract
This paper presents a convex recovery method for block-sparse signals
whose block partitions are unknown a priori. We first introduce a
nonconvex penalty function, where the block partition is adapted for the
signal of interest by minimizing the mixed l2/l1 norm over all possible
block partitions. Then, by exploiting a variational representation of
the l2 norm, we derive the proposed penalty function as a suitable
convex relaxation of the nonconvex one. For a block-sparse recovery
model designed with the proposed penalty, we develop an iterative
algorithm which is guaranteed to converge to a globally optimal
solution. Numerical experiments demonstrate the effectiveness of the
proposed method.