Research On Key Technologies Of Sparse-Representation-Based Image Decomposition And Image Completion

With the rapid development of imaging technology in last decades,digital images have become increasingly popular in various fields,and image processing has become one widely-used technique in plenty of applications.Cartoon-texture image decomposition and image completion are two important image processing problems,which are studied in this dissertation.Cartoontexture image decomposition refers to separating an image into a cartoon part that contains image structures and a texture part that contains self-similar patterns.It enables one to deal with image structures or texture patterns separately,with applications to motion estimation,stereo matching,etc.Image completion is about recovering the missing pixels from input images.It is a useful image restoration technique for removing salt-and-pepper noises,texts or scratches from images.Both image decomposition and image completion are ill-posed problems.In recent years,sparse representation has emerged as one popular unsupervised approach for solving ill-posed problems.This dissertation aims at proposing new sparse representation models and techniques for cartoon-texture image decomposition and image completion,which overcomes the weaknesses of the existing methods.Regarding image decomposition,most existing sparserepresentation-based methods ignore the patch recurrence in the texture part due to its selfsimilarity.We addressed this issue by designing new nonlocal sparsification transforms that can effectively exploit both the patch recurrence in both cartoon part and texture part,based on which an effective sparse model is proposed for image decomposition.Regarding image completion,existing dictionary learning models for sparse representation have either high computational cost or low expressive power when dealing with multi-dimensional and high-dimensional data,e.g.image sequences including videos,multi-spectral images,etc.Such issues become much more severe when using these dictionary learning approaches as the submodules of the image completion algorithm.To address such issues,a convolutional factorized dictionary learning model is proposed,based on which an image completion method with high performance and efficiency is developed.The contributions of the dissertation are as follows:1)A discriminative prior on patch recurrence is proposed.The traditional patch recurrence prior designed for image recovery only exploits the repeating property of image patches,without any consideration on the discrimination between cartoon components and texture components.The proposed prior considers the orientation characteristics of patch recurrence,which includes the isotropic patch recurrence prior for texture components and the anisotropic patch recurrence prior for cartoon components.As a result,it can well distinguish texture components from cartoon components,and avoid confusion on recurrent patches in patch-recurrence-based cartoon-texture decomposition approaches.2)A new image decomposition method is proposed.The proposed method can well describe the orientation characteristics of patch recurrence.With the proposed directional patch matching scheme and alternative patch stacking scheme,the dual sparse properties of the constructed stacks are deduced.Based on the dual sprase properties,a discriminative nonlocal sparse representation model is proposed,which can well exploit the differences of cartoon and texture in both local and nonlocal properties.The experimental results show that the proposed model can well distinguish the texture parts and the cartoon parts.3)A convolutional factorized dictionary construction scheme is proposed.Compared with the synthesis dictionary learning model,the proposed one uses an analysis form,which can update the sparse representation effectively.Compared with the patch-based model,the proposed one uses a convolutional form,which avoids the inconsistencies between pixels.Compared with the orthogonal dictionary learning model,the proposed one imposes orthogonality on each factor dictionary,which can learn an over-complete dictionary and update the dictionary effectively.Compared with the existing decomposition-based tensor dictionary learning approaches,the proposed one uses a convolutional factorization scheme,which avoids imposing rank-1 structures,leading to oriented atoms in the proposed dictionary.4)A dictionary-learning-based tensor completion method is proposed.The existing low-rankbased methods for visual tensor completion usually ignore the local structures of images,while the conventional dictionary-learning-based methods do not perform well either due to their limited effectiveness and expressive power.The proposed method is based on tensor dictionary learning,which can well exploit the local structures of images.The experimental results on four different datasets show that the proposed method not only outperforms the existing sparse-coding-based methods,but even outperforms the methods that combine sparse coding and low-rank approximation.This dissertation is of great significance to the development of sparse coding and dictionary learning technology,which can provide new ideas for the theory,models and algorithms of sparse representation.