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.
翻译:在 DCT 系数中恢复未知、缺失、损坏、扭曲或丢失的信息是数字图像处理的多种应用的共同任务,包括图像压缩、选择性图像加密和图像通信。 本文调查在数字图像的 DCT 系数中恢复特殊类型的信息: 符号位数 。 这个问题可以模拟成混合整数线性编程( MILP) 问题, 一般来说是NP- 硬的 。 为了有效地解决问题, 我们建议了两种近似方法 :(1) 基于放松的方法, 将 MILP 问题转换成线性编程( LP ) 问题 ; (2) 将目标图像分割和化方法分割到足够小的区域, 将目标图像分割到足够小的区域, 每一个都能够以 MIP 问题为主, 然后将全球优化的阶段化阶段, 以小的 MIP 问题或 LP 问题为模型, 来最大限度地提高各地区的平滑动性。 我们最先考虑的是, 如何使用全球优化来恢复 DCT 的标志性位数 。 我们考虑了如何将拟议方法应用到 eEG- enceral 的图像 和进行大范围的实验 。