An Improved Gradient Pursuit Algorithm for Signal Reconstruction Based on Compressed Sensing

Gradient Pursuit (GP) algorithm is one kind of the Greedy Algorithms for signal reconstruction. It is a practical method as a result of less computational requirements and better performance for signal reconstruction. GP algorithm is based on the steepest descent method of optimization theory. It uses the steepest descent step-size for the iterative reconstruction, which leads to the zigzag phenomenon and slow convergence. In this paper, improvements on the step-size for the original gradient pursuit algorithm are proposed by introducing Alternating Step-size (AS) and Shortened Step-size (SS). In order to measure the reconstruction quality of different algorithms, a new criterion called Matching Rate is defined in this paper. The experimental results show that the new method is superior to the Matching Pursuit (MP) algorithm and Orthogonal Matching Pursuit (OMP) algorithm. It could reconstruct the signal more accurately and rapidly than the available gradient pursuit method.