  This paper studies the joint support recovery of similar sparse vectors on
the basis of a limited number of noisy linear measurements, i.e., in a multiple
measurement vector (MMV) model. The additive noise signals on each measurement
vector are assumed to be Gaussian and to exhibit different variances. The
simultaneous orthogonal matching pursuit (SOMP) algorithm is generalized to
weight the impact of each measurement vector on the choice of the atoms to be
picked according to their noise levels. The new algorithm is referred to as
SOMP-NS where NS stands for noise stabilization. To begin with, a theoretical
framework to analyze the performance of the proposed algorithm is developed.
This framework is then used to build conservative lower bounds on the
probability of partial or full joint support recovery. Numerical simulations
show that the proposed algorithm outperforms SOMP and that the theoretical
lower bound provides a great insight into how SOMP-NS behaves when the
weighting strategy is modified.
