  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.
