Analysis of block coherence based on deterministic matrices

Abstract

In block compressed sensing, the retrieval of block sparse signals from an under determinedsystem of linear equations is of main interest. The successful recovery of such signals depends on the optimally designed sensing matrix with good coherence properties. Therefore, several families of matrices having optimal coherence properties with increased block size are required to be investigated. Such investigation will led to an improved block sparse signal reconstruction. 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 smaller the coherence parameters, better the recovery performance. Moreover, exploitation of block sparsity with certain conditions resulted in successful recovery for a higher sparsity level than treating the signal as conventionally sparse. The overall results confirmed that deterministicsensing matrices offer better results as compared to random sensing matrices.