Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical
imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant
dictionaries as sparsifying operators.
Algorithms (BOMP, BLOOMP) based on techniques of band exclusion and local optimization are proposed
to enhance Orthogonal Matching Pursuit (OMP) and deal with such coherent sensing matrices.
BOMP and BLOOMP have provably performance guarantee of reconstructing sparse, widely separated
objects independent of the redundancy and have a sparsity constraint and computational cost similar to
Numerical study demonstrates the effectiveness of BLOOMP for compressed sensing with highly coherent,
redundant sensing matrices.