Image Reconstruction Research Based On Nonconvex Local Convolutional Sparse Coding

With the explosive growth of people’s demand for image information,how to reconstruct high-quality images from less existing data has always been the focus of scholars,and image sparse reconstruction based on sparse representation can solve this problem well and is suitable for a variety of image processing tasks.The essential problem of image sparse reconstruction is sparse optimization,and the existing convolutional dictionary learning algorithm based on convex optimization can solve this problem under the premise of ensuring convergence,however,these convex optimization-based algorithms cannot obtain more sparse coded values,and the quality of image sparse reconstruction cannot be further improved.In view of this,this paper conducts an in-depth study of the convolutional dictionary learning algorithm based on nonconvex optimization,and successfully applies it to image sparse reconstruction.The main research contents of this paper are as follows:Firstly,this paper introduces the proximal alternating linearized minimization algorithm in the mathematical field into the sparse optimization problem,and combines the needle-based local convolutional dictionary processing strategy to propose a nonconvex nonsmooth local convolutional dictionary learning model and a nonconvex alternating local proximal algorithm for image sparse reconstruction.In order to improve the convergence speed of the algorithm,the adaptive parameters are introduced into the nonconvex alternating local proximal algorithm to form a backtracking process,and the adaptive nonconvex alternating local proximal algorithm is proposed.In order to focus on the verification of the advantages brought by nonconvex optimization,convex relaxation is used instead of nonconvex optimization,and the solution of convex optimization model is proposed by using convex alternating local proximal algorithm and adaptive convex alternating local proximal algorithm.Finally,the convergence of two nonconvex optimization algorithms is proved.The experimental results of image sparse reconstruction and cartoon texture image separation reconstruction show that the proposed adaptive nonconvex alternating local proximal algorithm has achieved better reconstruction performance than many mainstream reconstruction algorithms.Then,on the basis of the theory of nonconvex alternating local proximal algorithm,combined with inertial terms,an inertial nonconvex alternating local proximal algorithm for image sparse reconstruction is proposed,and the appropriate inertial term parameters can obtain higher reconstruction performance than the adaptive nonconvex alternating local proximal algorithm.The inertial term parameters are also applicable to convex optimization problems,so the inertial convex alternating local proximal algorithm based on the convex relaxation convolutional dictionary learning model is also proposed.The experimental results of image sparse reconstruction and image denoising show that the inertial nonconvex alternating local proximal algorithm can obtain higher quality reconstructed images.Finally,in view of the effective sparse reconstruction of the high-frequency components of the image by the nonconvex alternating local proximal algorithm,combined with the cartoon texture separation model,a compressed sensing model based on image separation and a compressed sensing image reconstruction algorithm are proposed for the compressed sensing natural image reconstruction.Combining this reconstruction algorithm with deep neural networks,a compressed sensing image separation network is proposed.The experimental results of compressed sensing natural image reconstruction show that under the low measurement rate,the proposed network has achieved better reconstruction performance than the current mainstream compressed sensing reconstruction network.