Proposed Algorithms Based on Accelerated Quantized Iterative Hard Thresholding for Compressed Sensing

Abstract

Compressive sampling (CS) is a signal recovery technique that can effectively recover a sparse signal using fewer measurements than its dimension. Different recovery algorithms such as convex optimization, greedy algorithms, and iterative hard thresholding are used for exact recovery. The iterative hard thresholding algorithms are faster than convex optimization for compressed sensing recovery problems. In this paper, three proposed algorithms are introduced. These three proposed algorithms are based on Accelerated Quantized Iterative Hard Thresholding (AQIHT). They are double-over-relaxation AQIHT (AQIHTDR), conjugate gradient AQIHT (AQIHTCG) and a conjugate gradient double-over-relaxation AQIHT (AQIHTCGDR). The double-overrelaxation algorithm (DR) is based on two over-relaxation steps and the conjugate gradient algorithm (CG) is based on computing the directional update and step size for efficient recovery. Extensive matlab simulation programs are executed to simulate the performance of the three proposed schemes. In addition, they are compared with the related ones. The performance metrics are signal to noise ratio (SNR), error (E) and iteration time. The proposed schemes have superior performance over the traditional ones. Moreover, the proposed mixed scheme has the best performance when compared to all other schemes.