Image Representation And Reconstruction Based On Sparse And Low Rank Theory

With the rapid development of digital and internet technology,image has become a main information carrier for people to acquire and utilize.Digital image processing technology has been widely applied in many fields of science and engineering.The effective acquisition,reconstruction and enhancement of digital images are the core issues that have been paid attention to in this field.The image signals have not only local similarity but also non-local similarity,leading to the sparse and low-rank characteristics,which provides an important basis for addressing many issues of image processing.As a new signal sampling theory proposed in recent years,the compressed sensing(CS)theory proves that if the signal is sparse,we can conduct dimensionality-reduced sampling and realize accurate reconstruction in the later stage.CS not only provides an excellent solution to achieve low cost and low delay acquisition of images,but also provides an effective idea to solve other image processing problems.CS has been widely concerned and deeply studied by scholars at home and abroad in various applications,such as medical imaging,image compression,image restoration and etc.Based on the above background,this paper conducted in-depth research on the image coding via compressed sensing,high-quality reconstruction of compressed sensing images,and super-resolution reconstruction of images,on the basis of the theories of sparse representation and low-rank decomposition of images.The main works include as follows:(1)exploration on adaptive image coding with CS based on image block transformation;(2)research on image compression perception reconstruction methods based on sparse and multi-sparse joint rules of non-local groups of images;(3)study on image super-resolution method based on non-local adaptive truncation of low-rank images.The highlights could be summarized as:1.This paper presents a compression sensing image coding method based on random permutation of block transform subband coefficients and human visual perception characteristics perception.In order to solve the problem of low sampling efficiency of the traditional image CS using non-adaptive projection transformation,an adaptive measurement matrix design method is presented based on the energy distribution characteristics of image block in DCT domain.Aiming at the problem of low measurement efficiency caused by the difference of sparsity of different blocks due to the non-stationary statistical characteristics of image,a compression sensing coding method based on random permutation of discrete cosine transform domain coefficients is proposed.The achievements could be further effectively used in robust image coding,encryption image coding and other applications.2.New CS image reconstruction methods based on adaptive group sparse representation with iterative reweighting are proposed.The inherent structural similarity in the image provides more new possibilities for sparse representation of image signals.Based on the non-local sparse theory of image,a new regularized CS reconstruction method using reweighting technique is developed.Firstly,the image similarity blocks are transformed by adaptive principal component analysis,then the transformation domain coefficients are weighted adaptively,and finally the sparse representation of the weighted coefficients is used to regularize reconstruction.By using the variational method,an iterative adaptive soft threshold filtering is proposed to solve the reconstruction model.The iterative reweighting reconstruction method proposed can effectively improve the image reconstruction quality becaused of adaptively restoring more high-frequency information.3.A standardized group sparse representation combining with total variation method,as well as a jointly multiple sparse representation regularization method,is proposed to regularize the image CS reconstruction.Considering the non-stationarity of natural image signals,the sparsity difference of different segmented image patch groups,and the different statistical distribution characteristics of different components in transform domain,a z-score normalized representation method is constructed and used for regularized compressed sensing image recovery.Firstly,adaptive sparse transformation is carried out on similar image blocks,then the component-level z-score standardized group sparse representation(ZSGSR)is performed,and finally the multi-sparse joint regularized CS reconstruction is implemented based on the ZSGSR combining with total variation(TV).By adaptive filtering of transform domain restoration,we could achieve much more detail information and thus improve the reconstructed image quality.4.An image super resolution(SR)method based on non-local adaptive truncation low rank representation is proposed.Based on the latent low rank characteristic of non-local similar image blocks,a new efficient image super-resolution model is constructed,where the entropy information of structurally similar blocks is computed,and used to estimate the target rank of low rank data matrix.The partial singular soft threshold algorithm is adopted to solve the SR model.Compared with the similar methods,the proposed method can get better SR performance.Theoretical analysis and extensive experimental results verify the effectiveness and efficiency of the proposed methods.