Studies And Applications On Sparse Representation Algorithm With Convolution

Sparse representation represents the main information of signal storage with a small number of non-zero atomic coefficients and simplifies the process of signal processing.On the traditional method of using the theory of sparse representation of image is studied mainly in relation to the separate coding of the image block,overlaping between block and block,and then ignored the image block has the characteristics of consistency.Using convolution sparse representation,the whole image is seen as a whole,sparse coding of the whole image,and the model is linearly approximating sparse signal by the sum of convolutions of the filters and corresponding feature maps.This paper mainly considers the algorithm of convolution sparse representation by sparse representation methods and sparse representation methods with convolution.The main contents are as follows:(1)Because traditional sparse reconstruction algorithm based on image block representation is not suitable for large scale images,we use convolutional matching pursuit(CMP)to approximate input signal and achieve the purpose of image convolution decomposition by controlling the residual.At the same time,under the condition of the sparse representation model,we use CMP algorithm which is combined with K-SVD algorithm to study a new group of filters and get a better effect of sparse approximation.(2)In the application of sparse representation in image reconstruction,the traditional method computes a group of overlapping image blocks independently.By using the sparse representation of the convolution,we take the image as a whole and code sparsely.As a result,the alternating direction multiplier method(CSR_ADMM)is used to approximate the input image,and the image is reconstructed.The experimental results show that the mechanism of convolution decomposition is moresuitable for image reconstruction.Then the parameters of the algorithm are discussed.