JPEG decompression can be understood as an image reconstruction problem similar to denoising or deconvolution. Such problems can be solved within the Bayesian maximum a posteriori probability framework by iterative optimization algorithms. Prior knowledge about an image is usually described by the l1norm of its sparse domain representation. For many problems, if the sparse domain forms a tight frame, optimization by the alternating direction method of multipliers can be very efficient. However, for JPEG, such solution is not straightforward, e.g., due to quantization and subsampling of chrominance channels. Derivation of such solution is the main contribution of this paper. In addition, we show that a minor modification of the proposed algorithm solves simultaneously the problem of image denoising. In the experimental section, we analyze the behavior of the proposed decompression algorithm in a small number of iterations with an interesting conclusion that this mode outperforms full convergence. Example images demonstrate the visual quality of decompression and quantitative experiments compare the algorithm with other state-of-the-art methods.

Standard decompression of JPEG images produces artifacts along edges and a disturbing checkerboard pattern. To reduce these artifacts, decompression can be formulated as an image reconstruction problem within Bayesian maximum a posteriori probability framework. In this type of problem, the prior information about an image is typically given by the l1norm of its sparse domain representation. In this paper, we show how the solution of this problem can be achieved very efficiently using the alternating direction method of multipliers if the sparsity domain forms a tight frame. The proposed algorithm restores images without disturbing JPEG artifacts in several iterations, typically considerably less than competing algorithms. The quality of reconstruction both visually and in terms of SNR primarily depends on the tight frame used.

We propose a method for removal of space-variant blur from images predominantly degraded by camera shake without any knowledge of camera trajectory. Blurs are first estimated in a small number of image patches. We derive a novel parametric blur interpolation method and discuss conditions under which it can be used to exactly calculate blurs for every pixel position. Having this information, we restore the sharp image by a standard regularization technique. Performance of the proposed method is experimentally validated.

We propose a solution to the problem of boundary artifacts appearing in several recently published fast deblurring algorithms based on iterated shrinkage thresholding in a sparse domain and Fourier domain deconvolution. Our approach adapts an idea proposed by Reeves for deconvolution by the Wiener filter. The time of computation less than doubles.

We propose a practical method to remove photo blur due to camera shake, which is a typical problem when taking photos in dim lighting conditions such as indoor or night scenes. We use a pair of images, one of them blurred and the other one underexposed or noisy because of high ISO setting. Existing methods assume convolution model, that is the same blur in the whole image. It is seldom true in practice, especially for wide angle lens photos. We apply a space-variant model of blurring valid in many real situations. Results are documented by a photograph of a night scene.

Functional properties of living tissues appear in PET, whereas structural information at significantly higher resolution and better image quality is provided by other modalities, such as CT or MRI. We illustrate how structural information of matched anatomic images can be used as priors in the total variation denoising and blind deconvolution of functional PET images. Experiments on phantom images and clinical data validate the proposed method.

In many real applications traditional superresolution methods fail to provide high-resolution images due to objectionable blur and inaccurate registration of input low-resolution images. In this paper, we present a method of superresolution and blind deconvolution of video sequences and address problems of misregistration, local motion and change of illumination. The method processes the video by applying temporal windows, masking out regions of misregistration, and minimizing a regularized energy function with respect to the high-resolution frame and blurs, where regularization is carried out in both the image and blur domains. Experiments on real video sequences illustrate robustness of the method.

We examine the problem of restoration from multiple images degraded by camera motion blur. We consider scenes with significant depth variations resulting in space-variant blur. The proposed algorithm can be applied if the camera moves along an arbitrary curve parallel to the image plane, without any rotations. The knowledge of camera trajectory and camera parameters is not necessary. At the input, the user selects a region where depth variations are negligible. The algorithm belongs to the group of variational methods that estimate simultaneously a sharp image and a depth map, based on the minimization of a cost functional. To initialize the minimization, it uses an auxiliary window-based depth estimation algorithm. Feasibility of the algorithm is demonstrated by three experiments with real images.