Alfred M. Bruckstein

Postprocessing of Compressed Images via Sequential Denoising

In this paper, we propose a novel postprocessing technique for compression-artifact reduction. Our approach is based on posing this task as an inverse problem, with a regularization that leverages on existing state-of-the-art image denoising algorithms. We rely on the recently proposed Plug-and-Play Prior framework, suggesting the solution of general inverse problems via alternating direction method of multipliers, leading to a sequence of Gaussian denoising steps. A key feature in our scheme is a linearization of the compression-decompression process, so as to get a formulation that can be optimized. In addition, we supply a thorough analysis of this linear approximation for several basic compression procedures. The proposed method is suitable for diverse compression techniques that rely on transform coding. In particular, we demonstrate impressive gains in image quality for several leading compression methods-JPEG, JPEG2000, and HEVC.

Motion-Compensated Coding and Frame Rate Up-Conversion: Models and Analysis

Block-based motion estimation (ME) and motion compensation (MC) techniques are widely used in modern video processing algorithms and compression systems. The great variety of video applications and devices results in diverse compression specifications, such as frame rates and bit rates. In this paper, we study the effect of frame rate and compression bit rate on block-based ME and MC as commonly utilized in inter-frame coding and frame rate up-conversion (FRUC). This joint examination yields a theoretical foundation for comparing MC procedures in coding and FRUC. First, the video signal is locally modeled as a noisy translational motion of an image. Then, we theoretically model the motion-compensated prediction of available and absent frames as in coding and FRUC applications, respectively. The theoretic MC-prediction error is studied further and its autocorrelation function is calculated, yielding useful separable-simplifications for the coding application. We argue that a linear relation exists between the variance of the MC-prediction error and temporal distance. While the relevant distance in MC coding is between the predicted and reference frames, MC-FRUC is affected by the distance between the frames available for interpolation. We compare our estimates with experimental results and show that the theory explains qualitatively the empirical behavior. Then, we use the models proposed to analyze a system for improving of video coding at low bit rates, using a spatio-temporal scaling. Although this concept is practically employed in various forms, so far it lacked a theoretical justification. We here harness the proposed MC models and present a comprehensive analysis of the system, to qualitatively predict the experimental results.

Image restoration via successive compression

In this paper we propose a method for solving various imaging inverse problems via complexity regularization that leverages existing image compression techniques. Lossy compression has already been proposed in the past for Gaussian denoising — the simplest inverse problem. However, extending this approach to more complicated inverse problems (e.g., deblurring, inpainting, etc.) seemed to result in intractable optimization tasks. In this work we address this difficulty by decomposing the complicated optimization problem via the Half Quadratic Splitting approach, resulting in a sequential solution of a simpler l2-regularized inverse problem followed by a rate-distortion optimization, replaced by an efficient compression technique. In addition, we suggest an improved complexity regularizer that quantifies the average block-complexity in the restored signal, which in turn, extends our algorithm to rely on averaging multiple decompressed images obtained from compression of shifted images. We demonstrate the proposed scheme for inpainting of corrupted images, using leading image compression techniques such as JPEG2000 and HEVC.

Reducing artifacts of intra-frame video coding via sequential denoising

In this work we propose a new postprocessing method for video sequences compressed using intra-frame coding techniques. The suggested method extends our previously published approach for handling compressed still-images. We rely on the Plug-and-Play Prior framework, which shows that a general inverse problem can be cast as a sequence of Gaussian denoising steps. We formulate the video recovery task as such an inverse problem, with a regularization that leverages on existing state-of-the-art video denoising algorithms. Our methods strength emerges from two origins: (i) the flexibility of using the best available video denoising algorithm; and (ii) the fact that, while intra-coding is treated, an inter-frame force is introduced via the denoising stage. As such, our scheme can be interpreted as belonging to the distributed video coding paradigm with an extended decompression procedure coupled with a relatively simple compression. A prominent part in our approach is a linearization of the nonlinear compression-decompression operation, while leveraging the intra-coding structure to obtain a block-diagonal matrix form. We demonstrate significant quality improvements for video sequences compressed using Motion-JPEG2000.