Research On Image Reconstruction Algorithm Based On Compressed Sensing

The sampling frequency is limited in more than two times the bandwidth of the signal according to the traditional Nyquist sampling theory to restruct the original signal accurately.Compressed Sensing is a kind of signal sampling theory in recent years, which can accurately reconstruct the original signal by collecting a small amount datas of the original signal. The theory of sampling and compression process synchronization break through limit of the traditional sampling method, which can successfully overcome the massive data sampling transmission and data storage problem to avoid the excessive waste of hardware resources.Application of Compressed Sensing theory is that a signal must be compressible or sparse,whose process mainly includes three aspects: signal sparse representation, the observed signal acquisition and reconstruction of the original signal. Signal reconstruction algorithm directly affecting the reconstruction quality, which can influence the Compressed Sensing signal processing ability.This article focuses on the in-depth study on the recovery of accurate image signal reconstruction algorithm, the main work is as follows:(1)Learn the basic principle of Compressed Sensing, and briefly introduces the research background and current situation, focusing on the observation matrix, reconstruction principle and algorithm, and analyzes the characteristics of mathematical reconstruction algorithm.With the greedy and L1 norm sparse convex optimization reconstruction algorithm by simulation experiment and comparative analysis of reconstruction results.(2)In this paper, the super resolution reconstruction concept and basic reconstruction algorithm based on compressed sensing theory framework is proposed based on improved projection onto convex sets reconstruction method, and the introduction of curvelet sparse transform and for the reconstruction of two-dimensional image data. By using the improved point spread function model updating reference frame, improve the reconstruction effect of pixels on the edge. At the every end of the projection onto convex sets to modify the signal,combining multi-scale and multi-orientation features of curvelet with the image of sparse optimization and threshold processing, and achieved the purpose of reconstruction image noise removal.(3) Image signal based on wavelet domain sparse, This paper select predefined filter and signal hard threshold on the observation results, stagewise orthogonal matching pursuit(stomp) algorithm is proposed when conjugate gradient descent algorithm is introduced, and the observed signal reconstruction with different compression ratios. In order to further verify the improved algorithm is applied to image reconstruction results, put forward the concept reconstruction image edge similarity. The simulation results show that compared with the improved St OMP algorithm, the improved St OMP algorithm in convergence time is very short, the reconstruction effect increased. The noise of reconstructed image was significantly reduced, PSNR value increased.