Blur kernel estimation and image restoration methods for blind deconvolution

Abstract

With the rapid development of mobile imaging devices, image has played the most important role in recording and sharing daily life. Since the imaging environment is very complex, such as noise, low light condition, object motion and camera motion due to its instability, it is very likely to introduce kinds of degradations in captured images, in which blur is one of the key degradation factors, severely limiting the visual perception and high level computer vision analysis. Image deblurring also named image deconvolution that aims at recovering clean image from its blurry observation is a hot topic in computer vision fields. Image deconvolution is an ill-posed inverse problem, due to the complex noises in the procedure of capture, transportation and storage. Since blur procedure is not known in practice, blind deconvolution is a more challenging task. The existing blind deconvolution methods usually include two stages, i.e., estimating blur kernel and non-blind deconvolution for recovering clean image, both facing bottlenecks in computational efficiency, robustness and restoration quality. To address these issues, we in this thesis will develop new restoration models along with efficient and effective optimization methods for robust image deblurring. (1) Efficient non-blind deconvolution is one key factor in guaranteeing high efficiency of blind deconvolution. We propose a novel image restoration model in gradient domain. Since gradient is more sparse than image, it is expected to achieve higher convergence rate. By incorporating with Total Variation model, we develop two fast optimization algorithms based on alternating direction method of multipliers (ADMM), resulting in derivative ADMM (D-ADMM) algorithms. D-ADMM algorithms can both converge to the global optimal solution, and is more computationally effcient than that in image domain. (2) As for blur kernel estimation, the existing methods usually borrow natural image priors. Then by carefully tuning parameters for each stage, trivial solution canbe avoided. We propose an iteration-wise priors framework for robust blur kernel estimation, in which image prior is modeled as hyper-Laplacian distribution and requires according prior parameters for each iteration. Furthermore, to avoid hand-crafted parameters tuning, we propose a discriminative learning framework to train iteration-wise parameters. Supervised by accurately estimating blur kernel, iteration-wise priors are trained to improve the robustness of blur kernel estimation, and can be widely applied in real world blurry images. (3) Despite the great progress in blind deconvolution, blur kernel estimation error is inevitable. The existing non-blind restoration methods, however, are developed with error free kernel assumption, making it very likely to introduce artifacts such as ringing effects and color distortions. To model blur kernel estimation error, we propose a novel partial deconvolution model for recovering high quality images. We first estimate reference Fourier spectrum from blurry image and then introduce a binary partial map to indicate the reliable Fourier entries of estimated blur kernel. During deconvolution only reliable Fourier entries are used, while adverse effect of blur kernel estimation error can be suppressed. By incorporating partial deconvolution into wavelet-based and learning-based restoration methods, high quality images can be recovered. (4) Furthermore, blur kernel estimation error by a certain blind deconvolution method has specifc property. It is very difficult to model blur kernel estimation error using a universal model for different blind deconvolution methods. We propose a simultaneous fidelity and regularization learning (SFARL) model, in which fidelity term models the residual caused by blur kernel estimation error. We employ a set of large size filters to extract spatial context in residual image, and then a set of non-linear functions are used to model the distribution of filters responses. As for a certain blind deconvolution method, we can establish abundant training samples, and then SFARL can be effectively trained for recovering high quality images. Moreover, SFARL can be applied to many other computer vision tasks, e.g., image denoising, removing rain streaks etc.