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.
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