A CONVOLUTIVE MIXING MODEL FOR SHIFTED DOUBLE JPEG COMPRESSION WITH APPLICATION TO PASSIVE IMAGE AUTHENTICATION Zhenhua Qu, Weiqi Luo, Jiwu Huang ∗ Guangdong Key Lab. of Information Security Technology Sun Yat-Sen University, Guangzhou, China, 510275 ABSTRACT The artifacts by JPEG recompression have been demonstrated to be useful in passive image authentication. In this paper, we focus on the shifted double JPEG problem, aiming at identi- fying if a given JPEG image has ever been compressed twice with inconsistent block segmentation. We formulated the shifted double JPEG compression (SD-JPEG) as a noisy convolu- tive mixing model mostly studied in blind source separation (BSS). In noise free condition, the model can be solved by directly applying the independent component analysis (ICA) method with minor constraint to the contents of natural im- ages. In order to achieve robust identification in noisy condi- tion, the asymmetry of the independent value map (IVM) is exploited to obtain a normalized criteria of the independency. We generate a total of 13 features to fully represent the asym- metric characteristic of the independent value map and then feed to a support vector machine (SVM) classifier. Experi- ment results on a set of 1000 images, with various parameter settings, demonstrated the effectiveness of our method. Index Terms— Image Forgery, Shifted Double JPEG, Con- volutive Mixing Model, ICA, Image Authentication 1. INTRODUCTION With the rapid advancement in digital image editing software, the verification the trustworthy of a given digital image is re- ceiving increasing concerns, especially in the legal system and journalism. The traditional approach of image authen- tication is to use digital signature and digital watermarking. However, these two methods will fail if the signature or wa- termark is not employed prior to the malicious editing of the untampered image. Recently, some researchers tried to ad- dress a new approach, called the Passive Image Authentica- tion which only uses the characteristic from the forgery/fake images to figure them out. Some pioneer works are done by Farid et al. and Fridrich et al. [1][2]. The JPEG recompression artifacts is one kind of those im- portant characteristics. It is unlikely for an ordinary JPEG ∗ This work is supported by NSFC (90604008, 60633030), NSF of Guang- dong (04205407), and 973 Program (2006CB303104). Contact Author (isshjw@mail.sysu.edu.cn) image/photo or a part of it to possess recompression artifacts, unless it has been opened and re-saved as JPEG format by an image editing software. Recent researches have been focusing on the Double JPEG Compression Problem 1 , which means to identify the image suffered from the lossy JPEG compres- sion twice. A possible solution for this problem presented by Lukas and Fridrich [2] is to estimate the primitive quantiza- tion table coefficients from a double compressed JPEG im- age directly. Other approaches tried to detect the abnormal DCT coefficient distribution caused by the recompression. In [1], Popescu and Farid utilized the periodical artifacts of the re-quantized DCT coefficient histogram. Fu et al. [3] con- tributed another identification algorithm based on a gener- alized Benford Law model of the blockwise discrete cosine transform (BDCT) coefficients. However the above meth- ods did not address how to determine whether a given JPEG image had been recompressed with inconsistent block seg- mentation which frequently occurs in a composite or region- duplication image. We define the task of identifying such a JPEG recompressed image with Shifted Double JPEG (SD- JPEG) Compression Problem. He et al. [4] noticed the dif- ference between these two types of problem and utilized it to detect forgery, but they did not derive any explicit model for the SD-JPEG problem. In previous work [5], we proposed an rapid identification algorithm in spatial domain based on the symmetric charac- teristic of blocking artifact characteristics matrix (BACM). In this paper, our contribution comes in three aspects : 1) We ad- dress a statistic model in the BDCT domain for the SD-JPEG problem and give it a new insight from the direction of BSS. 2) An novel ICA-based identification algorithm utilizing the symmetric property of IVM is proposed. 3) The problem of estimating the shifted distance is also addressed here to pro- vide detailed information of how the image is recompressed. The rest of this paper is organized as follows. In Sec- tion 2, we establish a convolutive mxing model of SD-JPEG compression. Section 3 mainly discusses the identification of the model with a ICA-based method and how to estimate the shifted distance. The experiment results with comparison to 1 Other than this literal explanation, this term has a more specific meaning which stands for unshifted double JPEG compression problem in this paper. 1661 1-4244-1484-9/08/$25.00 ©2008 IEEE ICASSP 2008