A Match Pursuit Based Method Adapted to Overcomplete Dictionary for Compressive Spectral Imaging

This paper proposes to introduce greedy pursuit, a conceptually simple hard thresholding pursuit algorithm called Signal Space Subspace Pursuit (SSSP) for calculating spare signal representations with overcomplete dictionaries whenever the sensing matrix (sampling operator) satisfies the Restricted Isometry Property adapted to Dictionary (D-RIP). Signal space greedy method has the ability to optimally compute (near) best projections that allow one to identify the most related a small number of dictionary atoms of an arbitrary signal in this setting. More practically, standard recovery algorithms are applicable to such projections while maintaining accurate signal recovery. Simulation results with a typical hyperspectral data set demonstrate the superiority of the proposed approach.