Phase Transition in Mixed l2/l1-norm Minimization for Block-Sparse Compressed Sensing

We have evaluated, via the replica method, phase transition thresholds for the mixed l(2)/l(1)-norm minimization applied to block-sparse compressed sensing with randomly generated measurement matrices. Our analysis takes into account that the matrix elements may be of non-zero mean, and shows that the phase transition threshold for the mixed l(2)/l(1)-norm minimization improves when the matrix elements have non-zero mean and the distribution of non-zero blocks of the target vector to be estimated has a certain imbalance.