Iterative Selection and Correction Based Adaptive Greedy Algorithm for Compressive Sensing Reconstruction

Abstract Compressive Sensing (CS) is a new sampling theory used in many signal processing applications due to its simplicity and efficiency. However, signal reconstruction is considered as one of the biggest challenge faced by the CS method. A lot of researches have been proposed to address this challenge, however most of the existing techniques start with the same forward step which does not provide the best reconstruction performance. In this paper, we aim to address this challenge by proposing an Adaptive Iterative Forward-Backward Greedy Algorithm (AFB). AFB algorithm is different from all other reconstruction algorithms as it depends on solving the least squares problem in the forward phase, which increases the probability of selecting the correct columns better than other reconstruction algorithms. In addition, AFB improves the selection process by removing the incorrect columns selected in the previous step. We evaluated the AFB’s reconstruction performance using two types of data: computer-generated data and real data set (Intel Berkeley data set). The simulation results show that AFB outperforms Forward-Backward Pursuit, Subspace Pursuit, Orthogonal Matching Pursuit, and Regularized OMP in terms of reducing reconstruction error.