A Gradient Pursuit Algorithm Based on Multi-Step Quasi-Newton Method

摘要

In order to solve the high computational complexity problem of gradient pursuit in compressed sensing, we applied multi-step quasi-Newton method to gradient pursuit and proposed a gradient pursuit algorithm based on multi-step quasi-Newton method (MSQN-GP). The MSQN-GP algorithm uses the pre-multiple gradient information to approximate the inverse matrix of the Hessian matrix of the objective function, and this scheme is applied to the gradient pursuit algorithm to efficiently solve the update direction problem, while avoiding complex matrix inversion operations. Firstly, we give a detailed theoretical derivation, which proved that the algorithm has both the decent property of the steepest descent method and the second-order convergence of the Newton method. Then, we present extensive simulation results to show that our proposed MSQN-GP algorithm can achieve significant reduction in complexity on the basis of ensuring reconstruction accuracy compared with the existing gradient pursuit algorithms.