Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Investigation of Sparsifying Transforms in Compressed Sensing for Magnetic Resonance Imaging with Fasttestcs

The goal of this contribution is to achieve higher reduction factors for faster Magnetic Resonance Imaging (MRI) scans with better Image Quality (IQ) by using Compressed Sensing (CS). This can be accomplished by adopting and understanding better sparsifying transforms for CS in MRI. There is a tremendous number of transforms and optional settings potentially available. Additionally, the amount of research in CS is growing, with possible duplication and difficult practical evaluation and comparison. However, no in-depth analysis of the effectiveness of different redundant sparsifying transforms on MRI images with CS has been undertaken until this work. New theoretical sparsity bounds for the dictionary restricted isometry property constants in CS are presented with mathematical proof. In order to verify the sparsifying transforms in this setting, the experiments focus on several redundant transforms contrasting them with orthogonal transforms. The transforms investigated are Wavelet (WT), Cosine (CT), contourlet, curvelet, k-means singular value decomposition, and Gabor. Several variations of these transforms with corresponding filter options are developed and tested in compression and CS simulations. Translation Invariance (TI) in transforms is found to be a key contributing factor in producing good IQ because any particular translation of the signal will not effect the transform representation. Some transforms tested here are TI and many others are made TI by transforming small overlapping image patches. These transforms are tested by comparing different under-sampling patterns and reduction ratios with varying image types including MRI data. Radial, spiral, and various random patterns are implemented and demonstrate that the TIWT is very robust across all under-sampling patterns. Results of the TIWT simulations show improvements in de-noising and artifact suppression over that of individual orthogonal wavelets and total variation ell-1 minimization in CS simulations. Some of these transforms add considerable time to the CS simulations and prohibit extensive testing of large 3D MRI datasets. Therefore, the FastTestCS software simulation framework is developed and customized for testing images, under-samping patterns and sparsifying transforms. This novel software is offered as a practical, robust, universal framework for evaluating and developing simulations in order to quickly test sparsifying transforms for CS MRI

Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First, from the perspective of image statistics, a joint statistical modeling (JSM) in an adaptive hybrid space-transform domain is established, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Second, a new form of minimization functional for solving image inverse problem is formulated using JSM under regularization-based framework. Finally, in order to make JSM tractable and robust, a new Split-Bregman based algorithm is developed to efficiently solve the above severely underdetermined inverse problem associated with theoretical proof of convergence. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions on Circuits System and Video Technology (TCSVT). High resolution pdf version and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM

Image restoration with group sparse representation and low‐rank group residual learning

Image restoration, as a fundamental research topic of image processing, is to reconstruct the original image from degraded signal using the prior knowledge of image. Group sparse representation (GSR) is powerful for image restoration; it however often leads to undesirable sparse solutions in practice. In order to improve the quality of image restoration based on GSR, the sparsity residual model expects the representation learned from degraded images to be as close as possible to the true representation. In this article, a group residual learning based on low-rank self-representation is proposed to automatically estimate the true group sparse representation. It makes full use of the relation among patches and explores the subgroup structures within the same group, which makes the sparse residual model have better interpretation furthermore, results in high-quality restored images. Extensive experimental results on two typical image restoration tasks (image denoising and deblocking) demonstrate that the proposed algorithm outperforms many other popular or state-of-the-art image restoration methods