Recovering Missing Coefficients in DCT-Transformed Images

TL;DR

This paper introduces a linear programming-based method for recovering missing DCT coefficients in images, demonstrating effectiveness especially when only the DC coefficient is missing, with potential applications in cryptanalysis.

Contribution

The work presents a novel optimization approach for DCT coefficient recovery, outperforming existing methods in specific scenarios and applicable to cryptanalysis and image processing.

Findings

Recovery quality decreases as more coefficients are missing

Method outperforms existing techniques when only the DC coefficient is missing

Effective on a large set of test images

Abstract

A general method for recovering missing DCT coefficients in DCT-transformed images is presented in this work. We model the DCT coefficients recovery problem as an optimization problem and recover all missing DCT coefficients via linear programming. The visual quality of the recovered image gradually decreases as the number of missing DCT coefficients increases. For some images, the quality is surprisingly good even when more than 10 most significant DCT coefficients are missing. When only the DC coefficient is missing, the proposed algorithm outperforms existing methods according to experimental results conducted on 200 test images. The proposed recovery method can be used for cryptanalysis of DCT based selective encryption schemes and other applications.