Design and Application of a Greedy Pursuit Algorithm Adapted to Overcomplete Dictionary for Sparse Signal Recovery

Abstract

Compressive sensing (CS) is a novel paradigm to recover a sparse signal in compressed domain. In some overcomplete dictionaries, most practical signals are sparse rather than orthonormal. Signal space greedy method can derive the optimal or near-optimal projections, making it possible to identify a few most relevant dictionary atoms of an arbitrary signal. More practically, such projections can be processed by standard CS recovery algorithms. This paper proposes a signal space subspace pursuit (SSSP) method to compute spare signal representations with overcomplete dictionaries, whenever the sensing matrix satisfies the restricted isometry property adapted to dictionary (D-RIP). Specifically, theoretical guarantees were provided to recover the signals from their measurements with overwhelming probability, as long as the sensing matrix satisfies the D-RIP. In addition, a thorough analysis was performed to minimize the number of measurements required for such guarantees. Simulation results demonstrate the validity of our hypothetical theory, as well as the superiority of the proposed approach.

An efficient algorithm for updating the penalty parameter of the alternating direction method for l1 problem

“…In the past, scholars have constructed some iterative algorithms to solve the above sparse optimization problems, such as interior point method [6] , proximal block coordinate homotopy method [7] , greedy algorithm [8][9][10] , gradient projection algorithm [11][12] , and fast iterative shrinkage-thresholding algorithm [13][14][15][16][17] . In 2012, Chen et al [18] developed a novel alternating direction approach, which focus on the problem from the view of variational inequality and a system of nonlinear equations.…”