Analysis of block coherence based on deterministic matrices

In block compressed sensing, the retrieval of block sparse signals i.e., sparse signal having nonzero entries in the form of blocks or clusters from an under determined system of linear equations is of main interest. The successful recovery of such signals depends on the sensing matrix. Therefore, it is desired to generate a sensing matrix with optimum block coherence for guaranteed recovery. The two coherence metrics i.e., block coherence and sub-coherence are important to analyze when considering the optimally designed sensing matrix. The implication of the outcome presented lies in the fact that exploitation of block sparsity with certain conditions results in successful recovery for a higher sparsity level than treating the signal as conventionally sparse. Moreover, deterministic matrix constructions based on optimum coherence allows for an increased number of blocks as compared to random matrix constructions consequently offering better reconstruction.