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

TL;DR

This paper presents two novel approximation methods for recovering sign bits of DCT coefficients in digital images, addressing an NP-hard optimization problem with improved performance over existing techniques.

Contribution

It introduces two new approximation approaches to solve the NP-hard problem of sign bit recovery in DCT coefficients, applicable to JPEG images.

Findings

Proposed methods outperform existing techniques in quality metrics.

Methods effectively recover sign bits in JPEG-encoded images.

Extensive experiments validate the superiority of the approaches.

Abstract

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.