Nonlinear regression A*OMP for compressive sensing signal reconstruction

A number of tree search based methods have recently been utilized for compressive sensing signal reconstruction. Among these methods, a heuristic algorithm named A* orthogonal matching pursuit (A*OMP) follows best-first search principle and employs dynamic cost model which makes sparse reconstruction exceptionally excellent. Since the algorithm performance of A*OMP relies heavily on preset parameters in the cost model and the estimation of these preset parameters requires a large number of experiments, there is room for improvement in A*OMP. In this paper, an improved algorithm referred to as Nonlinear Regression A*OMP (NR-A*OMP) is proposed which is built on the residue trend to avoid the estimation procedure. This method is inspired by the fact that the residue is correlated closely to the measurement matrix. The residue trend reflects the characteristics of nonlinear regression with the increasing of sparsity K. In addition, restricted isometry property (RIP) based general conditions are introduced to ensure the effectiveness and practicality of the algorithm. Numerical simulations demonstrate the superiority of NR-A*OMP in both reconstruction rate and normalized mean squared error. Results indicate that the performance of NR-A*OMP can become nearly equal to or even better than that of A*OMP with perfect preset parameters. (C) 2017 Elsevier Inc. All rights reserved.