Blind motion deblurring from a single image using sparse approximation

Abstract

Restoring a clear image from a single motion-blurred image due to camera shake has long been one challenging problem in digital imaging. Existing blind deblurring techniques either only can remove simple motion blurring, or need user interactions to work on more complex cases. In this paper, we present an approach to remove motion blurring from a single image by formulating the blind blurring as a new joint optimization problem, which simultaneously maximizes the sparsity of the blur kernel and the sparsity of the clear image under certain suitable redundant tight frame systems (curvelet system for kernels and framelet system for images). Without requiring any prior information of the blur kernel as the input, our proposed approach is able to recover high-quality images from given blurred images. Furthermore, the new sparsity constraints under tight frame systems enable the application of a fast algorithm called linearized Bregman iteration to efficiently solve the proposed minimization problem. The experiments on both simulated images and real images showed that our algorithm can effectively removing complex motion blurring from nature images.

Two-Phase Kernel Estimation for Robust Motion Deblurring

“…Lately, impressive progress has been made in estimating a complex motion blur PSF from a single image [1,3,6]. The success arises in part from the employment of sparse priors and the multi-scale framework.…”

“…The difference between this function and those used in [3,6] is on the definition of the regularization terms. Thresholding applies softly in our function through adaptive regularization, which allows the energy to concentrate on significant values and thus automatically maintains PSF sparsity, faithful to the deblurring process.…”

“…Deblurring is achieved through an alternating-minimization scheme. Cai et al [6] introduced a framelet and curvelet system to obtain the sparse representation for kernels and images. Levin et al [13] showed that common MAP methods involving estimating both the image and kernel likely fail because they favor the trivial solution.…”

“…The success of recent single-image methods partly stems from the use of various sparse priors, for either the latent images or motion blur kernels [1,3,6]. It was found that without these constraints, iterative kernel estimation is easily stuck in local minima and possibly results in a dense kernel and many visual artifacts in the restored image.…”

“…Notable progress has been made lately [1][2][3][4][5][6]. The blur process caused by camera shake is generally modeled as a latent image convolved with a blur point-spread-function (a.k.a.…”