Image Reconstruction Based On Optimization Of Measurement Matrix Of Compressed Sensing

Traditional signal samples follow the Nyquist sampling theorem,and the large amount of information in a modern complex signal,the sampling time required by Nyquist theory of sampling frequency is large,the sampling frequency requirement is high,it is difficult to achieve,so modern signal processing bottlenecks encountered.In recent years,the emergence of compressed sensing,completely breaking the limitations of Nyquist theorem,has opened a new chapter in the sampling theorem,which has broad application prospects.The basic idea of compressed sensing is to sample and compress sparse signals,sampling and compression performed simultaneously,then recover the original signal with the signal which is much smaller than the length of the sample values.Measurement matrix design is a key part of the compressed sensing,and the paper focuses the studying and analyzing on the Gaussian random measurement matrix.According to the design principles for observation matrix,design different weights to different part of the observation matrix,then optimizes the matrix using singular value decomposition method.In this paper,the effect of Compressed Sensing reconstructed image based on several sparse representation methods were analyzed and compared in image reconstruction results,proved the advantages of the above algorithm.Firstly,we discussed the compressed sensing theory,including sparse representation of the signal,the observation matrix design and reconstruction algorithms.Several sparse representation based on three traditional perception sparse representation algorithm simulated and analyzed respectively.Design principles for measurement matrix were analyzed,and gives several design methods of measurement matrix.Details of the principles and steps of several classic reconstruction algorithm were introduced.Secondly,we analyze the singular value decomposition,discussing the singular value decomposition theory,property and application.Finally,due to the need to satisfy the compressed sensing observation matrix properties(RIP)principle,namely the non-correlation between measurement matrix and sparse bases.According to inadequate of observation matrix,this paper presents a new algorithm-improved measurement matrix algorithm based on singular value decomposition.After sparse representation,the main information concentrated in the low frequency section,and theminority concentrated in the high frequency section,so increasing the several columns in the front of the measurement matrix can increase the sampling information.Since the smaller the maximum singular value of the matrix,the greater the incoherence.In this paper,singular value decomposition is applied to the observation matrix,so as to improve the reconstruction effect of the reconstructed image,so as to reach the purpose of improving the effectiveness of image reconstruction.The experimental results show that,the effect of the image reconstruction algorithm on different compression ratio has been increased,especially greater enhancement magnitude in the lower compression ratio.Compressed sensing image reconstruction using the observation matrix optimized,although the reconstructed time has increased,the rate of increase is very small.Compositing time and reconstruction precision,it is better than before.