Exploiting Image Local And Nonlocal Consistency For Mixed Gaussian-Impulse Noise Removal

Most existing image denoising algorithms can only deal with a single type of noise, which violates the fact that the noisy observed images in practice are often suffered from more than one type of noise during the process of acquisition and transmission. In this paper, we propose a new variational algorithm for mixed Gaussian-impulse noise removal by exploiting image local consistency and nonlocal consistency simultaneously. Specifically, the local consistency is measured by a hyper-Laplace prior, enforcing the local smoothness of images, while the nonlocal consistency is measured by three-dimensional sparsity of similar blocks, enforcing the nonlocal self-similarity of natural images. Moreover, a Split-Bregman based technique is developed to solve the above optimization problem efficiently. Extensive experiments for mixed Gaussian plus impulse noise show that significant performance improvements over the current state-of-the-art schemes have been achieved, which substantiates the effectiveness of the proposed algorithm.Comment: 6 pages, 4 figures, 3 tables, to be published at IEEE Int. Conf. on Multimedia & Expo (ICME) 201

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

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

Image Restoration for Remote Sensing: Overview and Toolbox

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS

Composite Minimization: Proximity Algorithms and Their Applications

ABSTRACT Image and signal processing problems of practical importance, such as incomplete data recovery and compressed sensing, are often modeled as nonsmooth optimization problems whose objective functions are the sum of two terms, each of which is the composition of a prox-friendly function with a matrix. Therefore, there is a practical need to solve such optimization problems. Besides the nondifferentiability of the objective functions of the associated optimization problems and the larger dimension of the underlying images and signals, the sum of the objective functions is not, in general, prox-friendly, which makes solving the problems challenging. Many algorithms have been proposed in literature to attack these problems by making use of the prox-friendly functions in the problems. However, the efficiency of these algorithms relies heavily on the underlying structures of the matrices, particularly for large scale optimization problems. In this dissertation, we propose a novel algorithmic framework that exploits the availability of the prox-friendly functions, without requiring any structural information of the matrices. This makes our algorithms suitable for large scale optimization problems of interest. We also prove the convergence of the developed algorithms. This dissertation has three main parts. In part 1, we consider the minimization of functions that are the sum of the compositions of prox-friendly functions with matrices. We characterize the solutions to the associated optimization problems as the solutions of fixed point equations that are formulated in terms of the proximity operators of the dual of the prox-friendly functions. By making use of the flexibility provided by this characterization, we develop a block Gauss-Seidel iterative scheme for finding a solution to the optimization problem and prove its convergence. We discuss the connection of our developed algorithms with some existing ones and point out the advantages of our proposed scheme. In part 2, we give a comprehensive study on the computation of the proximity operator of the ℓp-norm with 0 ≤ p \u3c 1. Nonconvexity and non-smoothness have been recognized as important features of many optimization problems in image and signal processing. The nonconvex, nonsmooth ℓp-regularization has been recognized as an efficient tool to identify the sparsity of wavelet coefficients of an image or signal under investigation. To solve an ℓp-regularized optimization problem, the proximity operator of the ℓp-norm needs to be computed in an accurate and computationally efficient way. We first study the general properties of the proximity operator of the ℓp-norm. Then, we derive the explicit form of the proximity operators of the ℓp-norm for p ∈ {0, 1/2, 2/3, 1}. Using these explicit forms and the properties of the proximity operator of the ℓp-norm, we develop an efficient algorithm to compute the proximity operator of the ℓp-norm for any p between 0 and 1. In part 3, the usefulness of the research results developed in the previous two parts is demonstrated in two types of applications, namely, image restoration and compressed sensing. A comparison with the results from some existing algorithms is also presented. For image restoration, the results developed in part 1 are applied to solve the ℓ2-TV and ℓ1-TV models. The resulting restored images have higher peak signal-to-noise ratios and the developed algorithms require less CPU time than state-of-the-art algorithms. In addition, for compressed sensing applications, our algorithm has smaller ℓ2- and ℓ∞-errors and shorter computation times than state-ofthe- art algorithms. For compressed sensing with the ℓp-regularization, our numerical simulations show smaller ℓ2- and ℓ∞-errors than that from the ℓ0-regularization and ℓ1-regularization. In summary, our numerical simulations indicate that not only can our developed algorithms be applied to a wide variety of important optimization problems, but also they are more accurate and computationally efficient than stateof- the-art algorithms