Convolutional Sparse Coding Theory And Image Reconstruction

Convolutional sparse coding has been widely used in tasks such as signal and image processing,image reconstruction and denoising.Traditional convolutional sparse coding is based on the Fourier domain to perform local operations on patch,ignoring the local features of the image.In order to make up for the limitations of convolutional sparse coding based on patch,slice-based convolutional sparse coding is proposed.This paper combines the idea of local processing based on slicing with the idea of deep learning to conduct a deeper study on the convolutional sparse coding model.Firstly,inspired by the idea of slice-based local processing and multi-layer convolutional sparse coding,this paper studies a new convolutional sparse coding model: slice-based multi-layer convolutional sparse coding.Based on this,a new multi-layer based pursuit algorithm is studied:a slice-based multi-layer fast iterative shrinkage threshold algorithm.Secondly,the local block coordinate descent algorithm is an effective method to solve the based pursuit problem of slice-based convolutional sparse coding,but there is no proof of the convergence of the local block coordinate descent algorithm.In this paper,the convergence theorem of the local block coordinate descent algorithm is given and theoretically proved.Based on slice-based multi-layer convolutional sparse coding and local block coordinate descent algorithm,a slice-based multi-layer local block coordinate descent algorithm(ML-LoBCoD)is studied.And give the convergence theorem and proof of the ML-LoBCoD algorithm.In addition,this paper studied two new convolutional sparse coding networks(CSCNetLFISTA)based on the learning fast iterative shrinkage threshold algorithm(LFISTA).Based on the worst-case bounds of the gradient map,the new LFISTA algorithm is derived using the step coefficients of the boundary-optimized near-end gradient method.The new CSCNet method not only maintains the computational simplicity of the original CSCNet method,but also has a global convergence rate.This paper proves that the new CSCNet method is superior to the original CSCNet method in theory and practice.Finally,this paper combines the residual structure with a CSCNet and studies a new type of deep learning model for CS-MRI,called the approximate residual convolutional sparse coding network(ARCSC-net).The ARCSC network studied in this paper was tested in pseudo radial sampling mode.Different methods were used to achieve MRI reconstruction on brain and knee data.Experiments show that the studied ARCSC network is superior to other latest technologies in terms of vision and quantification.