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

Nonparametric estimation of a point-spread function in multivariate problems

The removal of blur from a signal, in the presence of noise, is readily accomplished if the blur can be described in precise mathematical terms. However, there is growing interest in problems where the extent of blur is known only approximately, for example in terms of a blur function which depends on unknown parameters that must be computed from data. More challenging still is the case where no parametric assumptions are made about the blur function. There has been a limited amount of work in this setting, but it invariably relies on iterative methods, sometimes under assumptions that are mathematically convenient but physically unrealistic (e.g., that the operator defined by the blur function has an integrable inverse). In this paper we suggest a direct, noniterative approach to nonparametric, blind restoration of a signal. Our method is based on a new, ridge-based method for deconvolution, and requires only mild restrictions on the blur function. We show that the convergence rate of the method is close to optimal, from some viewpoints, and demonstrate its practical performance by applying it to real images.Comment: Published in at http://dx.doi.org/10.1214/009053606000001442 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Advanced Restoration Techniques for Images and Disparity Maps

With increasing popularity of digital cameras, the field of Computa- tional Photography emerges as one of the most demanding areas of research. In this thesis we study and develop novel priors and op- timization techniques to solve inverse problems, including disparity estimation and image restoration. The disparity map estimation method proposed in this thesis incor- porates multiple frames of a stereo video sequence to ensure temporal coherency. To enforce smoothness, we use spatio-temporal connec- tions between the pixels of the disparity map to constrain our solution. Apart from smoothness, we enforce a consistency constraint for the disparity assignments by using connections between the left and right views. These constraints are then formulated in a graphical model, which we solve using mean-field approximation. We use a filter-based mean-field optimization that perform efficiently by updating the dis- parity variables in parallel. The parallel updates scheme, however, is not guaranteed to converge to a stationary point. To compare and demonstrate the effectiveness of our approach, we developed a new optimization technique that uses sequential updates, which runs ef- ficiently and guarantees convergence. Our empirical results indicate that with proper initialization, we can employ the parallel update scheme and efficiently optimize our disparity maps without loss of quality. Our method ranks amongst the state of the art in common benchmarks, and significantly reduces the temporal flickering artifacts in the disparity maps. In the second part of this thesis, we address several image restora- tion problems such as image deblurring, demosaicing and super- resolution. We propose to use denoising autoencoders to learn an approximation of the true natural image distribution. We parametrize our denoisers using deep neural networks and show that they learn the gradient of the smoothed density of natural images. Based on this analysis, we propose a restoration technique that moves the so- lution towards the local extrema of this distribution by minimizing the difference between the input and output of our denoiser. Weii demonstrate the effectiveness of our approach using a single trained neural network in several restoration tasks such as deblurring and super-resolution. In a more general framework, we define a new Bayes formulation for the restoration problem, which leads to a more efficient and robust estimator. The proposed framework achieves state of the art performance in various restoration tasks such as deblurring and demosaicing, and also for more challenging tasks such as noise- and kernel-blind image deblurring. Keywords. disparity map estimation, stereo matching, mean-field optimization, graphical models, image processing, linear inverse prob- lems, image restoration, image deblurring, image denoising, single image super-resolution, image demosaicing, deep neural networks, denoising autoencoder