Research On Non-convex Image Restoration Algorithm Based On Tow Rank Prior

With the rapid development of information age,the applications of digital im-ages have become more and more extensi,ve,and the research in the field of dig-ital image processing has been greatly valued.Digital image restoration technol-ogy is one of the fundamental tasks in the field of image processing,with the goal of achieving a predetermined visual communication effect by image inpaint-ing.Digital image restoration technology plays an important role in low-level vi-sion(such as the restoration of ancient artifacts and old photographs)or in high-level intellisense(such as feature extraction and recognition).Image restoration is an inherently ill-posed inverse problem that has no well-defined unique solution.Therefore.it is avery necessary and crucial task to in-troduce reasonable prior information in the process of solving restoration opti-mization.At present,prior models on nat.ural image can be categorized into sev-eral categories:non-local smoothness,non-local similarity.non-Gaussian,sparsity and statistical probability distribution.Some traditional methods implement low rank matrix approximation based on the non-local similarity of image matri-ces.However.natural images are usually rich in texture and complex in struc-ture.and are of just.approximately low-rank.In this paper,the non-local similarity on patch level is used to process the image patches.and the optimization problem is solved based on the low-rank property of the matrix of similar patches rather than the whole image.Main research work and innovations are summarized as following aspects:(1)A low rank image restoration algorithm is proposed based on gradual regu-larization.Firstly,an image is divided into overlapping patches and we classify these patches into two categories;for each patch we search its similar patches by a similarity metric.Then we represent each similar patch as a column vector by concatenating all its columns,and stack them to obtain a patch matrix.Secondly,by introducing a low rank approximation algorithm based on gradual regularization,the low rank approximation of the patch matrix is realized.Finally.an estimated image is reconstructed by aggregating all pro-cessed patches with a weighted averaging scheme.Experiments on the filling of randomly missing pixels show that the proposed inpainting method not only dominates in the quantitative evaluation index,but also outperforms other related methods in terms of fine image structure preservation.(2)A low rank image restoration algorithm based on entropy function of singular values is proposed.Text overlay and scratch damage are another type of tasks for image restoration.Aiming at these damage characteristics,a low-rank ap-proximation algorithm based on entropy function of singular values is first introduced.Secondly,the aggregation step of patches is optimized.and a reg-ularization strategy is added in the iterative process.Experiments on scratch restoration and text removal show that the proposed method is superior to other competing methods in terms of fine image structure preservation.The restoration model based on the low rank prior fully utilizes the low rank property of the similar patch matrix,and recovers the main low-rank information of image,thus obtains a better image restoration.In a word,this research further strengthens the collaborative innovation of computational mathematics and in-formation science,deepens and enriches the research of image restoration tech-nology,which is expected to be further extended to research areas such as image super-resolution reconstruction.data cleaning,visual art communication and cul-tural heritage protection.