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

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

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

Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps

We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.Comment: 12 pages, 6 figure

From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration

In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underlying low-rank matrix directly from the corrupted observations, we progressively approximate the underlying low-rank matrix via minimizing the rank residual. Through integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we apply it to image restoration tasks, including image denoising and image compression artifacts reduction. Towards this end, we first obtain a good reference of the original image groups by using the image NSS prior, and then the rank residual of the image groups between this reference and the degraded image is minimized to achieve a better estimate to the desired image. In this manner, both the reference and the estimated image are updated gradually and jointly in each iteration. Based on the group-based sparse representation model, we further provide a theoretical analysis on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC model outperforms many state-of-the-art schemes in both the objective and perceptual quality

Wavelet/shearlet hybridized neural networks for biomedical image restoration

Recently, new programming paradigms have emerged that combine parallelism and numerical computations with algorithmic differentiation. This approach allows for the hybridization of neural network techniques for inverse imaging problems with more traditional methods such as wavelet-based sparsity modelling techniques. The benefits are twofold: on the one hand traditional methods with well-known properties can be integrated in neural networks, either as separate layers or tightly integrated in the network, on the other hand, parameters in traditional methods can be trained end-to-end from datasets in a neural network "fashion" (e.g., using Adagrad or Adam optimizers). In this paper, we explore these hybrid neural networks in the context of shearlet-based regularization for the purpose of biomedical image restoration. Due to the reduced number of parameters, this approach seems a promising strategy especially when dealing with small training data sets