Weak RIC Analysis of Finite Gaussian Matrices for Joint Sparse Recovery

This letter provides tight upper bounds on the weak restricted isometry constant for compressed sensing with finite Gaussian measurement matrices. The bounds are used to develop a unified framework for the guaranteed recovery assessment of jointly sparse matrices from multiple measurement vectors. The analysis is based on the exact distribution of the extreme singular values of Gaussian matrices. Several joint sparse reconstruction algorithms are analytically compared in terms of the maximum support cardinality ensuring signal recovery, i.e., mixed norm minimization, MUSIC, and OSMP based algorithms.