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 communication. This paper investigates the recovery of sign bits in DCT coefficients of digital images, by proposing two different approximation methods to solve a mixed integer linear programming (MILP) problem, which is NP-hard in general. One method is a relaxation of the MILP problem to a linear programming (LP) problem, and the other splits the original MILP problem into some smaller MILP problems and an LP problem. We considered how the proposed methods can be applied to JPEG-encoded images and conducted extensive experiments to validate their performances. The experimental results showed that the proposed methods outperformed other existing methods by a substantial margin, both according to objective quality metrics and our subjective evaluation.

翻译：在数字图像处理的多个应用场景中，包括图像压缩、选择性图像加密和图像通信等，恢复DCT系数中未知、缺失、损坏、畸变或丢失的信息是一项常见任务。本文研究了数字图像DCT系数中符号位的恢复问题，提出了两种不同的近似求解方法，用于解决一个通常属于NP难的混合整数线性规划（MILP）问题。第一种方法将MILP问题松弛为线性规划（LP）问题，第二种方法则将原始MILP问题分解为若干较小的MILP问题和一个LP问题。我们探讨了所提方法在JPEG编码图像中的应用，并通过大量实验验证了其性能。实验结果表明，无论是在客观质量指标还是主观评价方面，所提方法均显著优于现有其他方法。