1556-6013 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIFS.2014.2302078, IEEE Transactions on Information Forensics and Security IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 1 A Bayesian-MRF Approach for PRNU-based Image Forgery Detection Giovanni Chierchia, Giovanni Poggi, Carlo Sansone, Member, IEEE, and Luisa Verdoliva Abstract—Graphics editing programs of the last generation provide ever more powerful tools which allow to retouch digital images leaving little or no traces of tampering. The reliable detection of image forgeries requires, therefore, a battery of complementary tools that exploit different image properties. Techniques based on the photo-response non-uniformity (PRNU) noise are among the most valuable such tools, since they do not detect the inserted object but rather the absence of the camera PRNU, a sort of camera fingerprint, dealing successfully with forgeries that elude most other detection strategies. In this work we propose a new approach to detect image forgeries using sensor pattern noise. Casting the problem in terms of Bayesian estimation, we use a suitable Markov random field prior to model the strong spatial dependencies of the source, and take decisions jointly on the whole image rather than individually for each pixel. Modern convex optimization techniques are then adopted to achieve a globally optimal solution and PRNU estimation is improved by resorting to nonlocal denoising. Large- scale experiments on simulated and real forgeries show that the proposed technique largely improves upon the current state of the art, and that it can be applied with success to a wide range of practical situations. Index Terms—Image forgery detection, PRNU, sensor noise, Bayesian approach, Markov random fields. I. I NTRODUCTION D Igital images are more and more frequently used to support important decisions. This is especially true in the forensic field where, to make just a few examples, images are routinely used to describe the scene of a crime, or to define responsibilities in road accidents. Unfortunately, with the wide availability of sophisticated image manipulation tools, modifying a digital photo, with little or no obvious signs of tampering, has become easier than ever before [1]. Therefore, it is important to devise tools that help deciding on the authenticity of a digital image, which raises attention on the image forgery detection field. Several approaches have been proposed in the literature to detect image alterations under a variety of scenarios. A first category comprises active techniques, for image authentica- tion, based on the use of watermarks [2] and signatures [3], [4]. In the first case, the watermark is embedded into the image (possibly originating small distortions), while in the latter, Copyright (c) 2013 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. G.Chierchia is with Institut Mines-T´ el´ ecom; T´ el´ ecom ParisTech; CNRS LTCI, 75014 Paris, France. G.Poggi, C.Sansone and L.Verdoliva are with the DIETI, Universit` a Federico II di Napoli, Naples, Italy. E-mail: chierchi@telecom-paristech.fr, {giovanni.poggi, carlo.sansone, luisa.verdoliva}@unina.it. the signature is attached to the image as side information. Although these methods are very effective, they can be applied only when the digital source is protected at the origin, which is probably a minority of the cases of interest. Therefore, there has been a steadily growing interest on passive techniques which retrieve traces of manipulations from the image itself, with no need of collaboration on the part of the user. Some techniques are specifically tailored to copy-move forgeries, where portions of the image are cut and pasted elsewhere in the same image to duplicate or hide objects of interest. Duplicated parts are discovered by block-based processing or, more efficiently, by means of suitable invariant features [5], [6], [7]. A more general approach considers physical inconsistencies, such as the lighting of objects, shadows, or geometric features (dimension, position, etc.) of objects w.r.t. the camera [8], [9], [10]. Also, as many images are saved in some compressed JPEG format, several forgery detection techniques rely on the traces left by multiple JPEG compression. In fact, when a JPEG image is modified and saved again in JPEG format, specific artifacts appear as a result of the multiple quantization processes, suggesting the presence of some forms of tampering [11], [12], [13], [14]. Another valuable source of information is the acquisition phase, which often leaves peculiar traces, related to lens characteristics [15], [16], the color filter array (CFA) pattern [17], [18], [19], or the sensor array [20], [21], that can be used to discover image manipulations. In this latter context, the photo-response non uniformity (PRNU) noise appears as one of the most promising tools at hand. The PRNU arises from tiny imperfections in the silicon wafer used to manufacture the imaging sensor [22]. These physical differences provide a unique sensor pattern, specific of each individual camera, constant in time and independent of the scene. It can be therefore considered as a sort of camera fingerprint and used as such to accomplish forgery detection or image identification tasks. Indeed, the most common forms of image forgery, like copy-move or splicing, delete the original camera PRNU from the target region, a fact that can be detected through suitable analyses, provided the camera PRNU is available. Note that, unlike with most other approaches, the detection of tampering is based on the absence of the fingerprint, hence does not depend on the specific type of forgery. On the other hand, the PRNU pattern is fairly robust to several common forms of image processing, such as JPEG compression, filtering, or gamma correction [20], [21]. In [20] a PRNU-based technique for camera identification and forgery detection has been proposed, then refined in [21]. Given the potential of this algorithm [23], many research