Compressed Sensing Based on Trust Region Method

Abstract

Developed in recent years, compressed sensing (CS) has saved considerable data storage and time in signal acquisition and processing, drawing the attention of many scholars in various fields. At present, a key issue is the design of an effective CS reconstruction algorithm. Unlike the commonly used CS convex optimization approaches, which require determining the direction first and later using the linear search to attain the optimal displacement, the trust region method introduced into the CS model in this paper solves a quadratic convex optimization problem in the varied circular area. The simulated reconstruction of two-dimensional images is performed via MATLAB. Meanwhile, comparative analysis is executed using different CS reconstruction methods, such as the greedy algorithms (orthogonal matching pursuit, sparse adaptive matching pursuit) and convex optimization algorithms (basis pursuit, conjugate gradient). The experimental results are summarized and analyzed, demonstrating that the proposed CS trust region method may recover the images more accurately than state-of-the-art schemes.