Research Of 1 Bit Compressed Sensing Signal Reconstruction

Compressed Sensing theory is widely studied by scholars since birth date. By taking advantage of the sparsity of signal, get a small amount of measurements randomly when far below the Nyquist sampling rate, then reconstruct with high accuracy by non-linear reconstruction algorithm. Based on compressed sensing, 1 bit compressed sensing theory only preserves symbols of measurements, and reconstructs signals accurately by increasing number of measurements.This paper focuses on 1 bit compressed sensing theory. It deeply studies on matching sign pursuit reconstruction algorithm and Binary Iterative Hard Thresholding algorithm. and improved its shortcomings and deficiencies. According to above two study directions, this paper studies in detail on following aspects:1. Taking compressed sensing and 1 bit compressed sensing theory as the research model, and explain on three aspects: sparse Representation of signal, design of measurement matrix, study of reconstruction algorithm.2. We propose forward backward matching sign pursuit algorithm. This algorithm is based on matching sign pursuit, and import support set search pattern of FBP algorithm into matching sign pursuit algorithm, thus introduce the forward backward matching sign pursuit algorithm, which aims to solve adaptive reconstruction problems when sparsity is unknown. The experiments show that the forward backward matching sign pursuit algorithm not only can achieve the blind reconstruction of signal, but also decrease the running time of algorithm.3. We propose block binary iterative hard thresholding algorithm. This algorithm import block sparse model into binary iterative hard thresholding algorithm, introduce BLOCK-BIHT algorithm which by taking each block as unit, divide the signals into blocks to decrease the signal sparsity and preserve the structure of signal, thus decrease the number of calculation. The experiments show that compared with the BIHT algorithm in case of low bits, the BLOCK-BIHT algorithm has better reconstruction accuracy.