Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed l1/l2 Regularization

The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the l1/l2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term, on an application to seismic data blind deconvolution.Comment: 5 page

Generalized Video Deblurring for Dynamic Scenes

Several state-of-the-art video deblurring methods are based on a strong assumption that the captured scenes are static. These methods fail to deblur blurry videos in dynamic scenes. We propose a video deblurring method to deal with general blurs inherent in dynamic scenes, contrary to other methods. To handle locally varying and general blurs caused by various sources, such as camera shake, moving objects, and depth variation in a scene, we approximate pixel-wise kernel with bidirectional optical flows. Therefore, we propose a single energy model that simultaneously estimates optical flows and latent frames to solve our deblurring problem. We also provide a framework and efficient solvers to optimize the energy model. By minimizing the proposed energy function, we achieve significant improvements in removing blurs and estimating accurate optical flows in blurry frames. Extensive experimental results demonstrate the superiority of the proposed method in real and challenging videos that state-of-the-art methods fail in either deblurring or optical flow estimation.Comment: CVPR 2015 ora

Understanding Kernel Size in Blind Deconvolution

Most blind deconvolution methods usually pre-define a large kernel size to guarantee the support domain. Blur kernel estimation error is likely to be introduced, yielding severe artifacts in deblurring results. In this paper, we first theoretically and experimentally analyze the mechanism to estimation error in oversized kernel, and show that it holds even on blurry images without noises. Then to suppress this adverse effect, we propose a low rank-based regularization on blur kernel to exploit the structural information in degraded kernels, by which larger-kernel effect can be effectively suppressed. And we propose an efficient optimization algorithm to solve it. Experimental results on benchmark datasets show that the proposed method is comparable with the state-of-the-arts by accordingly setting proper kernel size, and performs much better in handling larger-size kernels quantitatively and qualitatively. The deblurring results on real-world blurry images further validate the effectiveness of the proposed method.Comment: Accepted by WACV 201

Light Field Blind Motion Deblurring

We study the problem of deblurring light fields of general 3D scenes captured under 3D camera motion and present both theoretical and practical contributions. By analyzing the motion-blurred light field in the primal and Fourier domains, we develop intuition into the effects of camera motion on the light field, show the advantages of capturing a 4D light field instead of a conventional 2D image for motion deblurring, and derive simple methods of motion deblurring in certain cases. We then present an algorithm to blindly deblur light fields of general scenes without any estimation of scene geometry, and demonstrate that we can recover both the sharp light field and the 3D camera motion path of real and synthetically-blurred light fields.Comment: To be presented at CVPR 201

Discriminative Transfer Learning for General Image Restoration

Recently, several discriminative learning approaches have been proposed for effective image restoration, achieving convincing trade-off between image quality and computational efficiency. However, these methods require separate training for each restoration task (e.g., denoising, deblurring, demosaicing) and problem condition (e.g., noise level of input images). This makes it time-consuming and difficult to encompass all tasks and conditions during training. In this paper, we propose a discriminative transfer learning method that incorporates formal proximal optimization and discriminative learning for general image restoration. The method requires a single-pass training and allows for reuse across various problems and conditions while achieving an efficiency comparable to previous discriminative approaches. Furthermore, after being trained, our model can be easily transferred to new likelihood terms to solve untrained tasks, or be combined with existing priors to further improve image restoration quality