Research On Sparse Representation Based Image Compressive Sensing Reconstruction Algorithm

As the latest signal processing technology in the early 21 st century,compressed sensing breaks the strict requirements of Nyquist sampling theorem on sampling rate,and samples and compresses the signal at the same time.The compressed sensing uses the signal with sparsity or can be sparse expressed in a certain domain,obtains a small number of measured values through the observation matrix,and then reconstructs the original signal according to the measured values and reconstruction algorithm.Since recovering the original signal from a small number of observations is an ill-posed problem and no unique solution can be obtained,high-precision image reconstruction can be achieved by making full use of the prior information of the image.In this thesis,based on image sparse representation of prior information,the reconstruction algorithm is studied in depth.The innovation achievements are as follows:1.The image compressed sensing reconstruction algorithm based on group sparse representation only considers the sparsity and non-local similarity of the image,but does not consider the local smoothness of the image,as a result,the details of the image are over-smoothed,to solve the above problems,an image compression sensing reconstruction algorithm based on group sparse representation and weighted full variation is proposed in this thesis.The algorithm considers three prior information of signal sparsity,nonlocal similarity and smoothness,and to solve this problem that the traditional weighted total variation model uses global weighting to introduce error information,a new weighting strategy is adopted,which only sets the weight for the high-frequency components of the image,it is conducive to the protection of image details.In addition,using the hard threshold modulus square method is used to better protect the non-principal component coefficients.The experimental results show that the performance of the proposed algorithm is better than that of the mainstream compressed sensing reconstruction algorithm,the peak signal to noise ratio and structural similarity are improved.2.For the sparse representation of fixed basis leads to the poor adaptability of the algorithm,and the reconstruction accuracy of the algorithm is not high for 1 norm optimization,an image compressed sensing reconstruction algorithm based on p norm is proposed in this thesis.Firstly,the sparsity and nonlocal self-similarity of the image are transformed into regular terms,design a nonlocal regularization model based on p norm,then designs an sparse basis by singular value decomposition algorithm,the sparse basis can better protect the fine texture part of the image;finally,we use the split Bregman iterative algorithm and the generalized soft threshold algorithm to solve the proposed algorithm efficiently.The experimental results show that the performance of the proposed algorithm is better than that of the mainstream compressed sensing reconstruction algorithm,the peak signal to noise ratio and structural similarity are improved,the peak signal-to-noise ratio is 8.14 d B higher than that of the image reconstruction algorithm based on discrete cosine transform.