Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Comparison of super-resolution algorithms applied to retinal images

A critical challenge in biomedical imaging is to optimally balance the trade-off among image resolution, signal-to-noise ratio, and acquisition time. Acquiring a high-resolution image is possible; however, it is either expensive or time consuming or both. Resolution is also limited by the physical properties of the imaging device, such as the nature and size of the input source radiation and the optics of the device. Super-resolution (SR), which is an off-line approach for improving the resolution of an image, is free of these trade-offs. Several methodologies, such as interpolation, frequency domain, regularization, and learning-based approaches, have been developed over the past several years for SR of natural images. We review some of these methods and demonstrate the positive impact expected from SR of retinal images and investigate the performance of various SR techniques. We use a fundus image as an example for simulations

Robust Algorithms for Low-Rank and Sparse Matrix Models

Data in statistical signal processing problems is often inherently matrix-valued, and a natural first step in working with such data is to impose a model with structure that captures the distinctive features of the underlying data. Under the right model, one can design algorithms that can reliably tease weak signals out of highly corrupted data. In this thesis, we study two important classes of matrix structure: low-rankness and sparsity. In particular, we focus on robust principal component analysis (PCA) models that decompose data into the sum of low-rank and sparse (in an appropriate sense) components. Robust PCA models are popular because they are useful models for data in practice and because efficient algorithms exist for solving them. This thesis focuses on developing new robust PCA algorithms that advance the state-of-the-art in several key respects. First, we develop a theoretical understanding of the effect of outliers on PCA and the extent to which one can reliably reject outliers from corrupted data using thresholding schemes. We apply these insights and other recent results from low-rank matrix estimation to design robust PCA algorithms with improved low-rank models that are well-suited for processing highly corrupted data. On the sparse modeling front, we use sparse signal models like spatial continuity and dictionary learning to develop new methods with important adaptive representational capabilities. We also propose efficient algorithms for implementing our methods, including an extension of our dictionary learning algorithms to the online or sequential data setting. The underlying theme of our work is to combine ideas from low-rank and sparse modeling in novel ways to design robust algorithms that produce accurate reconstructions from highly undersampled or corrupted data. We consider a variety of application domains for our methods, including foreground-background separation, photometric stereo, and inverse problems such as video inpainting and dynamic magnetic resonance imaging.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143925/1/brimoor_1.pd

Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented

A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods

Accurate Light Field Depth Estimation with Superpixel Regularization over Partially Occluded Regions

Depth estimation is a fundamental problem for light field photography applications. Numerous methods have been proposed in recent years, which either focus on crafting cost terms for more robust matching, or on analyzing the geometry of scene structures embedded in the epipolar-plane images. Significant improvements have been made in terms of overall depth estimation error; however, current state-of-the-art methods still show limitations in handling intricate occluding structures and complex scenes with multiple occlusions. To address these challenging issues, we propose a very effective depth estimation framework which focuses on regularizing the initial label confidence map and edge strength weights. Specifically, we first detect partially occluded boundary regions (POBR) via superpixel based regularization. Series of shrinkage/reinforcement operations are then applied on the label confidence map and edge strength weights over the POBR. We show that after weight manipulations, even a low-complexity weighted least squares model can produce much better depth estimation than state-of-the-art methods in terms of average disparity error rate, occlusion boundary precision-recall rate, and the preservation of intricate visual features

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