Robust primary quantization step estimation on resized and double JPEG compressed images

As one of the most important forensic tasks, reconstruction of the original information in tampered images is a key step for tampering detection and localization. Currently, a number of methods have been designed to estimate the primary quantization steps of double compressed JPEG images. However, the estimation in the presence of resizing operation remains a challenge. In this paper, we propose a robust primary quantization steps estimation method on resized and double JPEG compressed images. Specifically, the distribution of Discrete Cosine Transform (DCT) coefficients is firstly analyzed on the inverse resized image. Then, a maximum likelihood function together with a filtering strategy is designed to obtain the primary quantization step on Alternating Current (AC) bands. In addition, we find the prominent peak in the Discrete Fourier Transform (DFT) spectrum of the distribution of Direct Current (DC) coefficients is nonlinearly related to the step. Based on this observation, a mapping function derived from the geometric fitting is proposed to estimate the step on DC band. Experimental results demonstrate the proposed method provides superior estimation performance.