IEEE SIGNAL PROCESSING LETTERS, VOL. 23, NO. 5, MAY2016 693 Sensor Pattern Noise Estimation Using Probabilistically Estimated RAW Values Ambuj Mehrish, Member, IEEE, A. V. Subramanyam, Member, IEEE, and Sabu Emmanuel, Member, IEEE Abstract—Photo response nonuniformity (PRNU) is consider as reliable camera fingerprint for identifying source of a digital images. Digital cameras use various image processing operations to map linear color measurements (raw data) into nonlinear narrow gamut image. This nonlinear transformation affects esti- mation of PRNU. To undo the effect of nonlinear transformation, in this letter, we propose to estimate PRNU from probabilistically obtained raw values. Since not all cameras provide raw values as their output, we propose to compute estimate of raw values from the JPEG images using probabilistic color derendering procedure. The estimated raw values are modeled as a Poisson process and then maximum likelihood estimation (MLE) is used for PRNU esti- mation. The experimental results show that, the digital camera identification using our proposed PRNU estimate is better than using other popular PRNU estimate. Index Terms—Digital forensics, maximum likelihood estimation (MLE), photo response nonuniformity (PRNU), Poisson process, raw data, source identification. I. I NTRODUCTION D IGITAL camera technology has seen rapid development in the past decade. A large number of digital images are produced everyday using various cameras. Due to dramatic advancement in imaging and computing technologies, it is of utmost importance for law enforcement agencies to identify the camera used for capturing the image provided as evidence in a court of law. Various techniques for digital camera identification are pro- posed in the recent years [1]–[9], [15]–[19]. Among them, identification using photo response nonuniformity (PRNU) is commonly used. In [1], Lukáš et al. proposed to use wavelet denoising filter to denoise the original image and obtain camera reference pattern using several such images. Normalized corre- lation coefficient is then used to determine if a given image is from a reference camera. Since PRNU is multiplicative noise, Chen et al. [2] use maximum likelihood estimation (MLE) for estimation of multiplicative factor from reference images. Effect of denoising filter is investigated in [3] by Cortiana et al. The authors proposed sparse three-dimensional (3-D) trans- form domain collaborative filtering for more accurate noise extraction. Sutcu et al. [4] extended the work presented in [1] Manuscript received March 23, 2016; revised February 25, 2016; accepted March 24, 2016. Date of publication March 30, 2016; date of current version April 12, 2016. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jiwu Huang. A. Mehrish and A. V. Subramanyam are with the Department of Electronics and Communication Engineering, Indraprastha Institute of Information Technology, New Delhi 110020, India (e-mail: ambujm@iiitd.ac.in; subramanyam@iiitd.ac.in). S. Emmanuel is with the Department of Computer Science, Kuwait University, Kuwait City 13060, Kuwait (e-mail: sabu@cs.ku.edu.kw). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LSP.2016.2549059 by incorporating camera’s demosaicing characteristics into the decision process, which enhances and increases the accuracy. There have been various attempts to improve the accuracy of digital camera identification [5]–[8], [20]–[27]. In [5], Li et al. showed that it is desirable and necessary to preprocess the sensor noise to suppress unwanted artifacts for better relia- bility. Lin et al. in [6] perform preprocessing on reference SPN via a spectrum equalization. They also propose to enhance SPN via filtering distortion removal in [7]. Hu et al. [8] proposed an enhanced method to extract camera sensor pattern noise (SPN). They assume that the large component of a camera SPN is more reliable and thus should be used in correlation detection while the other components should be discarded. Hu et al. in [9] further expanded their work from a single color channel (e.g., green channel) to three color (RGB) channels. Although all the aforementioned references have used images of various formats for source camera identification, using raw data has not been deeply investigated. The authors of [10] investigate the problem of identifying the source imaging device of the same model using sensor data. Their approach is based on the Poisson–Gaussian noise model for describing the distribution of the given image. In their paper, they proposed to used two parameters obtained from same model and can act as unique fingerprint for a camera. However, these camera fin- gerprints can distinguish between different models but are not discriminative for devices of the same camera model. In this letter, we propose an algorithm for estimation of PRNU from probabilistically estimated raw values. 1 First, we obtain the estimate of raw values from corresponding JPEG images using a probabilistic approach developed in [11]. We then use a joint Poisson probability model to define the distri- bution of raw values. In order to estimate the PRNU component of the camera, we use MLE and estimate of true value obtained from noisy raw value using a denoising algorithm [12]. We per- form experiments on a wide gamut of images from a composite database and evaluate its performance against a popular cam- era identification algorithm [1] and [24]. To the best of our knowledge, this is the first letter which extracts PRNU from probabilistically estimated raw values. The experimental results show that the digital camera identification using our proposed PRNU estimate is better than using the PRNU estimate of [1] or [24]. This is because the proposed method uses probabilis- tically estimated raw values. Since these raw values are close to the values captured by sensor without undergoing significant image processing camera pipeline, the PRNU estimate is better than other image formats such as JPEG. This letter is organized as follows. In Section II, we describe the proposed algorithm, followed by discussion in Section III. In Section IV, we demonstrate the performance of the proposed 1 Raw values refer to probabilistic estimate obtained using corresponding decompressed JPEG values for each pixel. 1070-9908 © 2016 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.