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.