Recovering Sign Bits of DCT Coefficients in Digital Images as an Optimization Problem

Recovering unknown, missing, damaged, distorted or lost information in DCT coefficients is a common task in multiple applications of digital image processing, including image compression, selective image encryption, and image communications. This paper investigates recovery of a special type of information in DCT coefficients of digital images: sign bits. This problem can be modelled as a mixed integer linear programming (MILP) problem, which is NP-hard in general. To efficiently solve the problem, we propose two approximation methods: 1) a relaxation-based method that convert the MILP problem to a linear programming (LP) problem; 2) a divide-and-conquer method which splits the target image into sufficiently small regions, each of which can be more efficiently solved as an MILP problem, and then conducts a global optimization phase as a smaller MILP problem or an LP problem to maximize smoothness across different regions. To the best of our knowledge, we are the first who considered how to use global optimization to recover sign bits of DCT coefficients. We considered how the proposed methods can be applied to JPEG-encoded images and conducted extensive experiments to validate the performances of our proposed methods. The experimental results showed that the proposed methods worked well, especially when the number of unknown sign bits per DCT block is not too large. Compared with other existing methods, which are all based on simple error-concealment strategies, our proposed methods outperformed them with a substantial margin, both according to objective quality metrics (PSNR and SSIM) and also our subjective evaluation. Our work has a number of profound implications, e.g., more sign bits can be discarded to develop more efficient image compression methods, and image encryption methods based on sign bit encryption can be less secure than we previously understood.Comment: 13 pages, 8 figure

Exploiting spatial smoothness to recover undecoded coefficients for transform domain distributed video coding

In a transform domain distributed video coding scheme, the correlation between the current encoding unit, e.g. block and slice, and the corresponding side-information is modeled using a virtual channel. This correlation model is then used for rate allocation, quantization, and Wyner-Ziv coding. Since the encoder can only have an estimate of the correlation instead of the exact knowledge of the side-information, the decoder will fail to recover the quantized transformed coeffi- cients with a nonzero probability. In this paper, we propose to integrate a scheme at the decoder to recover the undecoded coefficients using the spatial smoothness property of individual video frames. Simulation results demonstrated that, at different decoding failure probabilities, a transformed coeffi- cient recovery scheme can significantly improve the quality of videos in terms of both PSNR and SSIM

A maximum likelihood approach to video error correction applied to H.264 decoding

Video error concealment has long been identified as the last line of defense against transmission errors. This is especially true for real time video communication systems where retransmissions are rarely used because of timing constraints. Since error handling is outside the scope of video coding standards, decoders may choose to simply ignore the corrupted packets, or attempt to decode their content. Video error correction is a viable alternative to deal with transmission errors when corrupted packets reach their destination. Until now, these approaches have received little considerations. This is mainly because the proposed methods either rely on specific coding tools or constraints, or require far too many computations compared to video error concealment techniques. In this thesis, we propose a novel video error correction method based on maximum likelihood decoding. The method estimates the likeliest syntactically valid video slice content based on the erroneous video packets rather than discarding the content, and concealing the missing information. Such content is obtained by combining the likelihood of the candidate codewords with the bit modification likelihood associated to each candidate. We propose two solutions centered around our maximum likelihood decoding approach. First, we introduce a slice-level video error correction method. Furthermore, we show how to integrate the soft-output information shared by the channel decoder to evaluate the bit modification likelihood. We also show that it is possible to use our maximum likelihood decoding approach when soft-output information is not available. Then, we refine the solution at the syntax-element-level. The final solution we obtain can be used in real-time communication systems as it is computationally inexpensive compared to the slice-level solution, or the solutions proposed in the literature. Our final solution is then applied to the correction of videos conforming to the H.264 Baseline profile. We selected three 720x480 sequences, five 704x576 sequences, and one 720x576 sequence to run simulations. Each sequence was coded at a target bitrate of 1 Mbps, 1.2 Mbps, and 1.5 Mbps. All 27 sequences were then submitted to a noisy channel with a bit error rate ranging from 10−5 to 10−3. Our 5400 observations show a PSNR improvement of 1.69 dB over the video error concealment method implemented in the H.264 reference software. Furthermore, our results also indicate a 0.42 dB PSNR improvement over state-of-the-art error concealment STBMA+PDE