Sparse Low-rank And Subspace Prior Information For Image Restoration

Image processing especially in the field of image restoration,most algorithms focus on nonlocal sparse representation and exploit valuable image prior information.For the strong correlation between similar image feature patches or image feature cubes,it can minimize the rank of matrix or tensor to solve the low-rank approximation.Sparse low-rank constraint and subspace prior information are wildely used in the field of image processing as well as are the key point of image restoration.For the applications of sparse low-rank constraint and subspace prior information in image restoration,this research discusses the theorys and algorithms of image restoration.As an extension of the thesis,the paper makes a research on color-to-gray conversion based on subapsce.The main innovations are listed as follow:(1)For image inpainting,the proposed detail-preserving image inpainting algorithm adopts the low rank regularization to gradient similarity minimization,namely that we employ the low rank constraints in the horizontal and vertical gradients of the image and then reconstruct the desired image using the adaptive iterative singular-value thresholding of both derivatives.Experimental results consistently demonstrate that the proposed algorithm works well for both structural and texture images and outperforms other techniques,in terms of both objective and subjective performance measures.(2)For the remote sensing images reconstruction,this chapter resorts to the reference prior information between bands to build a generalized nonconvex low-rank approximation framework.Then it solves the nonlocal model of low-rank prior information via the conjugate gradient method,approximated by first-order Taylor expansion,and singular value threshold.Experimental results demonstrate the proposed algorithm improves several dBs in terms of peak signal to noise ratio(PSNR)and preserves image details significantly compared to most of the current approaches.The proposed method can restore the texture structure and reconstruct remote sensing image accuraly with less measured data.(3)For the image deburling and compressive sensing image reconstruction,this work is committed to achieving the goal by convoluting the target image with Filed-of-Experts(FoE)filters to formulate multi-feature images.Then similarity-grouped cube set extracted from the mul-ti-features images is regarded as a low-rank tensor.Then we present a multi-filters guided low-rank tensor coding(MF-LRTC)model for image restoration.Furthermore,we extend the MF-LRTC model by employing continued non-convex norm to promote its efficiencies(MF-NLRTC).The resulting MF-LRTC model and non-convex MF-NLRTC model are addressed by efficient ADMM technique.Using such a low-rank tensor coding would reduce the redundancy between feature vectors at neighboring locations and improve the efficiency of the overall sparse representation.The potential effectiveness of this tensor construction strategy is demonstrated in image restoration including image deblurring and compressive sensing(CS)applications.(4)For image decolorization,on the assumption that a good gray conversion should make the conveyed gradient values to be maximal,this work presents a two-step strategy to efficiently extend the parameter searching solver for the two-order multivariance polynomial model,adapts the three weighting parameters in this first-order linear model with discrete searching solver.On the other hand,we present a maximum weighted projection function,incorporating weights of the original gradients into the maximization problem.The Gaussian weighted factor consisting of the gradients of each channel of the input color image is employed to better reflect the degree of preserving feature discriminability and color ordering.Extensive experimental evaluations on the existing datasets show that the proposed methods outperforms the state-of-the-art methods quantitatively and qualitatively.In summery,based on signal processing,this thesis focus on sparse low-rank constraint and subspace prior information and proposes three image restoration algorithms and two decolorization methods.The proposed menthods can effectively overcome the limitations of the existing methods and achieve better performance on image inpainting,reconstruction,deblurring,and decolorization,providing a new approach to image restoration.