Researth On Compressed Sensing Image Reconstrution And Denoising Algorithm

Compressed Sensing(CS)is a new signal sampling and processing theory based on Matrix analysis,Probability and statistics,Functional Analysis and Topology and other basic disciplines,It is based on a priori sparse characteristics of the signals and achieves data compression while sampling signals.Its Sampling frequency can be much lower than the Nyquist sampling rate,which realizes the efficient effective "direct access to information".CS mainly includes three aspects: the sparse representation of the signal,the construction of the measurement matrix and the design of the reconstruction algorithm.Compared with the traditional way,Compressed Sensing theory breaks through in the signal acquisition and processing and has broad application prospects.In this paper,the two-dimensional image signal is researched,the research results and the main innovation points include the following four aspects.Firstly,we propose a new reconstruction algorithm with self-healing capabilities based on the compressed sensing for the image signal.After an analysis of the factors of degraded quality of the image,we constructed a new mathematical model of the degradation of the image.By improving representation of image sparse and measurement matrix in the image compressed sensing system,a new algorithm about image reconstruction is presented.Due to the up sampling and fuzzy operation of the inverse process of improving measurement matrix,the process of image reconstruction has the function of self repairing.The simulation results show the effectiveness of the new reconstruction algorithm.Secondly,we researched a new compressed sensing denoising algorithm,which is based on anisotropic multi-scale geometric transformation.In the existing compressed sensing algorithms for the reconstruction image,the TV filter for removing noise can not both reduce noise and keep the details.Referring to the design of discrete shear filter,we constructed a new geometric transformation of the tight framework of anisotropic multi-scale image to achieve the optimal image sparse representation,and used an improved SALSA algorithm in the process of reconstructing the image.Simulation results show that the algorithm is able to reconstruct an image from the observation with a small amount of noise pollution,and to eliminate noise effectively with little distortion at the edges and small details of the image.Compared with the existing compressed sensing denoising algorithm,the new algorithm has obvious improvement in the effect of thesubjective and objective image.Thirdly,we researched a denoising algorithm based on compressive sensing for the noise removal from multi-focus image.In the processing of multi-focus image denoising,the reconstruction of the efficient image information contained in the high-frequency component is realized by compressed sensing,and anti-plus is realized by the use of residual.We avoided filtering out too much useful image information in the process of denoising while not knowing the noise variance.The denoising effect is improved by the algorithm.We researched a image recovery algorithm for the speckle noise polluted image based on the combination of the homomorphic filtering and median filtering.Our algorithm is a fusion of the two classical denoising algorithms,and achieves the advantages of the two complementary algorithms.It can remove speckle noise effectively and improve the image quality.The simulation results show that its performance is significantly better than single homomorphic filtering or median filtering algorithm.