A Novel Fourier-based Approach for Camera Identiﬁcation

Vittoria Bruni

, Silvia Marconi

and Domenico Vitulano

Department of Basic and Applied Sciences for Engineering, Sapienza Rome University,

via Antonio Scarpa 14-16, 00161 Rome, Italy

Keywords:

Camera Identiﬁcation, PRNU, Fourier Transform.

Abstract:

In this paper the source camera identiﬁcation problem is considered and novel features for PRNU noise are

studied. The regularity of a suitable sampling of the PRNU image is considered and it is measured through

the decay of its Fourier spectrum. This single global feature is independent of image ﬁltering and size, but

it carries signiﬁcant information concerning the image. The aim is to use this feature in the classiﬁcation

step. Some preliminary results show that this kind of approach is promising as it is able to reach identiﬁcation

scores that can be comparable to the reference source camera identiﬁcation method, without requiring any

image downsampling or cropping.

1 INTRODUCTION

The increasing use of images and videos in sev-

eral multimedia applications has offered new research

challenges and problems. One of the most interest-

ing is Image Forensic, due to the crucial role of im-

ages and videos for several investigation purposes,

such as identiﬁcation of the sources that took images,

authenticity, robustness of data transmission, storage

and manipulation — just to cite a few. Among the

aforementioned problems, probably the most fasci-

nating is camera identiﬁcation (Al-Ani and Kheliﬁ,

2017; Lukas et al., 2006) as having several implica-

tions in forensics (Chen et al., 2008; Chierchia et al.,

2010; Korus and Huang, 2016). Coarsely speaking,

it mainly consists of looking for a reliable correspon-

dence between a given image and the device that took

it. One of the most adopted (and powerful) tools for

camera identiﬁcation is PRNU (Photo Response Non

Uniformity noise). It consists of a noise component

in any acquired image that is caused by the CCD im-

perfections, so that particular pixels are susceptible to

giving brighter intensities than others. This peculiar-

ity plays a crucial role as it is a sort of ﬁngerprint of

the device that in principle makes it easy to recognize.

Unfortunately, this is not the case as it is very difﬁcult

to extract PRNU from a given image. That is why a

https://orcid.org/0000-0003-3909-7463

https://orcid.org/0000-0002-4916-4896

https://orcid.org/0000-0001-6088-9743

Figure 1: Block scheme of the whole pipeline for camera

identiﬁcation problem.

plethora of approaches has been proposed in the last

years concerning this topic.

Coarsely speaking, camera identiﬁcation problem

can be seen from two different points of view: foren-

sic and scientiﬁc. Keeping in mind forensics require-

ments, it is possible to give a coarse taxonomy of the

proposed approaches (Caldelli et al., 2018; Chierchia

et al., 2014; Korus and Huang, 2016; Marra et al.,

2017; Valsesia et al., 2017) by considering the most

frequent cases, brieﬂy described below:

1. given a set of available devices and an image ac-

quired by one of them, the goal consists of looking

for which device took the image;

Bruni, V., Marconi, S. and Vitulano, D.

A Novel Fourier-based Approach for Camera Identiﬁcation.

DOI: 10.5220/0010437000990106

In Proceedings of the International Conference on Image Processing and Vision Engineering (IMPROVE 2021), pages 99-106

ISBN: 978-989-758-511-1

2. given a set of available devices and an image, the

goal consists of determining whether the device

taking that image belongs to such a set;

3. given a set of images, the goal is to group them

according to the corresponding source.

Sometimes, the requirements above can be relaxed

and it may be sufﬁcient to solve subproblems such

as to ﬁnd out only the brand or the model - rather than

the speciﬁc device. From a scientiﬁc/practical point

of view, the problems above necessarily require two

main steps: PRNU extraction and PRNU comparison

(via a suitable metric). With regard to PRNU extrac-

tion, several approaches adopt denoising techniques

that allow to get the noise (i.e., PRNU) in terms of the

residual image. PRNU comparison represents an even

more difﬁcult task because of PRNU noisy nature —

for approaches belonging to this class that mainly fo-

cus on clustering, see for instance (Georgievska et al.,

2017; Huang et al., 2015; Marra et al., 2017). To fur-

ther complicate the problem, distortions introduced

by image upload/download from the social networks

have to be accounted for, as they often represent the

actual available data (Caldelli et al., 2018; Valsesia

et al., 2017). Fig. 1 depicts the whole source camera

identiﬁcation pipeline. It is evident that each block

in the pipeline gives a contribution to the ﬁnal result

in terms of error. For instance, PRNU extraction usu-

ally employs a classical denoising process — as in

the pioneering work of Lukas et al. (Lukas et al.,

2006). Since denoising is not perfect, as a side effect

one achieves a mix of PRNU and image components

that usually alters the ﬁnal result. Even though differ-

ent and more sophisticated approaches have been pro-

posed in the literature (Akshatha et al., 2016; Al-Ani

and Kheliﬁ, 2017; Salvi and Vitulano, 2019; Fridrich,

2009; Tiwari and Gupta, 2018; Kumar and Hasse-

brook, 1990; Li et al., 2018; Thaia et al., 2015; Xu

et al., 2016; Zhao et al., 2019), the problem still holds.

On the other hand, PRNU comparison is delicate due

to the impulsive (and quasi random) nature of PRNU.

It is straightforward that in the camera identiﬁcation

problem a cumulative error occurs and it is difﬁcult to

separate and quantify the contribution of each speciﬁc

phase.

In this paper we step back to reformulate the prob-

lem as the following subproblem. Speciﬁcally, we

work on ﬂat ﬁelds images, i.e. those representing

a uniform and ﬂat background — thus mainly con-

taining PRNU. This assumption, although simplis-

tic, allows us to by-pass all problems due to network

uploading/downloading and PRNU extraction. The

(sub)problem we aim to address is: which is the best

way to represent and compare two PRNUs? Although

simpler, it remains a hard problem because two noisy

signals have to be compared. If they have no distor-

tion, the correlation method proposed in (Lukas et al.,

2006) is very performing. Unfortunately, this is not

the real case in practice. Hence, the question is now

if it is possible to differently represent PRNU in order

to use classical image processing tools to get better

results. To this aim, a different PRNU representation

is proposed. It consists of suitably rearranging it in

order to increase its visual regularity. A simple exam-

ple is shown in Fig. 2. The interesting aspect of this

approach is twofold. On the one hand, the resulting

image is more intellegible from a visual point of view;

on the other hand, this image is more ”tractable” by

means of classical signal processing tools. In par-

ticular, the decay of the Fourier spectrum is consid-

ered as representative of the global signal regularity,

and it has been used as single feature in the source

identiﬁcation process, as described in the ﬁrst case of

forensics requirements listed at the beginning of this

section. Even if this is a ﬁrst attempt to give a dif-

ferent representation of a PRNU signal, to the best

of the authors knowledge, it has various advantages:

i) it reaches comparable performance to the classi-

cal correlation approach in (Lukas et al., 2006) when

comparing images having the same size, even if just

one global spectrum parameter rather than the whole

PRNU image is employed; ii) it is independent of the

image size so that no resinzing or cropping is required

for comparing device PRNU and image PRNU (more

realistic scenario).

Preliminary results have been achieved on the

publicly available Dresden database (Gloe and Bhme,

2010) and identiﬁcation results have been studied in

different conditions. Particular attention has been de-

voted to the ability of the single global feature to cor-

rectly assign each image to the corresponding device;

as it will be shown, the estimation of this parameter

on different regions of the image allows us to deﬁne

an array of features that contributes to further increase

identiﬁcation performance.

The remainder of the paper is the following. Next

section presents the proposed method along with

some theoretical and practical motivations. Section 3

presents some preliminary experimental results, while

the last section draws the conclusions.

2 THE PROPOSED MODEL

In the literature, the observed image is modelled as

J(x, y) = I(x, y)+ I(x, y)K(x, y) + N(x, y),

where J is the acquired image, (x, y) the pixel loca-

tion, I is the original image content, K is the PRNU

IMPROVE 2021 - International Conference on Image Processing and Vision Engineering

100

Figure 2: Two different PRNU representations: Top: Con-

ventional PRNU matrix, Bottom: PRNU matrix whose val-

ues have been sorted row-wise and then column-wise.

component while N represents other noise sources

that are independent of K (Lukas et al., 2006). K is

a zero-mean noise component that is independent of I

and it is speciﬁc for the device that took the image J.

As it can be observed, the original image plays

a crucial role in the equation above and then the ex-

traction of K is a very delicate operation and active

research ﬁeld. However, if an almost constant image

is acquired, we get a ﬂat ﬁeld (FF) image that can be

brieﬂy written as

J(x, y) = B + BK(x, y) + N(x, y),

where B denotes the constant background. Despite

the presence of the noise component N, FF image bet-

ter reveals K. That is why, whenever possible, ﬂat

ﬁeld images are used for estimating device PRNU,

i.e. the reference pattern. The common procedure

for K estimation is described below and it also char-

acterizes the most famous and pioneering approach

for source camera identiﬁcation presented in (Lukas

et al., 2006).

A set of m images having almost constant back-

ground is acquired, i.e.

(x, y) = B

+ B

(x, y) + N

(x, y), i = 1, .., m;

a denoiser F is applied to each J

and the residual im-

age is extracted, i.e. R

= J

− F(J

). Since the im-

ages J

, i = 1, ..., m have been acquired by the same

device and the noise sources N

are iid, then K can

be estimated either as a simple pixelwise mean of the

estimated residuals R

or through the maximum like-

lihood estimator, i.e. K =

∑

i=1

∑

i=1

. The latter method

is more robust and it allows for a more accurate esti-

mation of the reference pattern.

The same denoising procedure is applied when-

ever the PRNU from a single image has to be ex-

tracted. In order to assess if an image W has been

taken by a given device, the normalized correla-

tion between the estimated reference pattern K and

the residual R for the image W is computed, i.e.

ρ(K, R) =

, where σ

is the cross correlation

between K and R, while σ

and σ

are the standard

deviations of K and R respectively. The closer to 1

ρ, the higher and more reliable the match between the

image W and the device having K as reference pattern.

Even though this kind of approach provides sat-

isfying results, the use of correlation implies a per-

fect match between K and R dimension; if it is not

the case, some resizing/cropping is required but this

would cause the modiﬁcation of noise component or

misalignments between the comparing noise compo-

nents. In addition, correlation values are in general

close to zero as the denoising process cannot perfectly

separate PRNU from the remaining noise sources. Fi-

nally, the accuracy of correlation decreases whenever

the original image has been altered by some opera-

tions, as for example, the upload or download from

the web or social networks. That is why in this pa-

per we are interested in contributing to solve the ﬁrst

problem. i.e. to ﬁnd novel features for K image that

can be used independently of the image size. For the

same reason, ﬂat ﬁelds images will be analysed.

The decreasing/increasing rearrangement is a well

known concept in mathematics (Duff, 1967) but it is

also used in signal processing as rank ordering for

continuous-time signals (Ferreira, 2001). It consists

of a sorted version of the original signal. In a more

formal setting, the decreasing rearrangment f

∗

of f

is deﬁned as the inverse of the cumulative distribu-

tion of the function f . As a result, f

∗

is a function

having some nice properties and relations with the

original one; more precisely, it preserves some in-

teresting properties of f , such as mean, energy, dis-

tribution function and global regularity — see (Duff,

1967; Ferreira, 2001) for details. In the studied case,

the function f is the image K and we are interested

in studying and exploiting the properties of its sorted

counterpart K

∗

. In particular, we empirically ob-

served that K

∗

, that has been deﬁned by rearrang-

ing the values of K in increasing order along the x

(rows) and y (columns) direction, shows some geo-

metrical structures that seem to characterize the sin-

gle device. An example is shown in Fig. 3, where

∗

of distinct devices are depicted. As it can be ob-

served, these sorted images present a peculiar pattern

that allows for discriminating between different de-

A Novel Fourier-based Approach for Camera Identiﬁcation

101

Figure 3: Top: Device. Bottom: corresponding rearranged

PRNU matrix K

∗

for three different devices belonging to

three different brands.

vices. In fact, for each considered device, a differ-

ent pattern is observable, while for the same device,

the same pattern is provided by distinct ﬂat ﬁeld im-

ages, as Fig. 4 shows. We then conclude that the

characterization of the observed pattern enables the

characterization of the device and, in particular, it can

contribute to discriminating images acquired by dif-

ferent devices. This observation motivates our work

whose aim is then to deﬁne features for the observed

behaviour.

In particular, if we design an ideal straight line

from the topleft corner to the bottommost right one,

i.e. the diagonal of the rectangular image domain, we

get a signal that captures most of the observed geo-

metrical structure, as Fig. 5 shows. Hence, the aim

Figure 4: Rearranged ﬂat ﬁeld images acquired by the same

device. The ﬁrst device in Fig. 3 has been considered.

is to provide a feature of the resulting signal and to

evaluate to what extent it is able to represent/identify

the whole reference PRNU. To this aim we made the

following observations:

• the geometrical patterns are mainly characterized

by a different frequency of the repeated struc-

tures (sort of pseudospherical waves having spe-

ciﬁc wavelength). We then expect that this kind

of feature is mainly emphasized and measurable

in the signal spectral components;

• one of the main feature of a function is its regular-

ity that can be measured through its global Lips-

chitz exponent;

• the decay of the Fourier spectrum is stricly corre-

lated to signal global Lipschitz exponent.

It turns out that the decay of the modulus of the

coefﬁcient of the Fourier transform of the diagonal of

the rank sorted matrix K

∗

of the PRNU image is the

feature that is worth to investigate. In the sequel f (y)

will identify the intensity signal corresponding to the

diagonal of the rectangular K

∗

domain.

2.1 Fourier Spectrum Decay as PRNU

Feature

One of the main features of a function is its regularity.

The latter can be referred to the whole function, i.e.

IMPROVE 2021 - International Conference on Image Processing and Vision Engineering

102

Figure 5: Intensity signal corresponding to the diagonal of

the rectangular domain of K

∗

. Plots are referred to the blue

color channel of the images depicted in Fig. 3.

global regularity, or it can be considered locally (lo-

cal regularity). Independently of its kind, regularity

can be measured as the Lipschitz regularity (Mallat,

1998). We recall that a function f is uniformly Lips-

chitz over an interval [a, b] of the real axis if for each

y ∈ [a, b] there exist a positive constant C independent

of y and a polynomial p

of degree bαc such that

∀ v ∈ [a, b] | f (v) − p(v)| ≤ C|y − v|

. (1)

If α < 1, then α characterizes the singularity type.

Furthermore, if f (y) is the signal under study,

f (ω)

its Fourier transform, ω the frequency, and if

f (ω)| ≤

1 + ω

1+q+δ

, (2)

Figure 6: Loglog plot of the Fourier spectrum of the Inten-

sity signals in Fig. 5 (gray line). The estimated straight line,

as in eq. (3), using the ﬁrst 10% frequencies, except for the

DC term, is also depicted (black line).

with C and δ two positive constants, then f is smooth

and q is the order of smoothness. The same result

holds whenever the smoothness is measured in terms

of Lipschitz exponent α. As a result, by measuring

the asymptotic decay of the modulus of the Fourier

transform of the signal f , we get some information

concerning its global regularity.

Based on these results, we consider the global Lip-

schitz exponent α of f and, without loss of generality,

we relax the relation in eq. (2) as |

f (ω)| ≤

|ω|

1+α+δ

By taking the logarithm to both members, we get

log(|

f (ω)|) ≤ log(C) − (1 + α + δ)log(|ω|) (3)

so that α regulates the slope of a straight line that

A Novel Fourier-based Approach for Camera Identiﬁcation

103

bounds the logarithm of the absolute value of the

Fourier transform. Hence, a least squares regression

on log(|

f (ω)|) allows for the estimation of the slope

of the straight line, and then α — see Fig. 6.

It is worth observing that the regularity measured

in the sorted signal is not independent of the regularity

of the original signal so that the estimated regularity

is strictly related, in some sense, to the regularity of

the original PRNU (Ferreira, 2001). This observation

further motivates the choice of focusing on the prop-

erties of the rank sorted matrix. On the other hand,

α is a global feature, but eq. (1) also holds locally.

Hence, in order to better characterize the analyzed

PRNU image, the same Lipschitz exponent estima-

tion procedure can be applied on subregions of the

whole image. In this way a more local information is

embedded in the estimated Lipschitz coefﬁcients and

a vector of features can be deﬁned for the image under

study. The components of this features vector are the

Lipschitz coefﬁcients estimated on each image subre-

gion Ω

, j = 1, ..., M. In this paper, rectangular subre-

gions have been considered by partitioning the image

into sub-blocks having the same size.

2.2 The Algorithm

Before presenting the proposed source identiﬁcation

algorithm in details, it is worth observing that, each

color channel can be processed separately and the co-

efﬁcients estimated for each color channel, respec-

tively α

, α

, deﬁne the feature vector associated

to PRNU image. The second observation is the fol-

lowing. K regularity can be estimated directly from

ﬂat ﬁeld images by excluding the highest spectrum

frequencies, where the contribution of the noise com-

ponent N cannot be considered negligible. In this way

we do not need to estimate the reference pattern K for

each device, but the corresponding features vector can

be directly estimated as

∑

i=1

R,i

, α

∑

i=1

G,i

, α

∑

i=1

B,i

(4)

where α

∗,i

is the Lipschitz exponent of the * color

channel of the ﬂat ﬁeld image J

. In other words, for

each color channel, the average of the regularity coef-

ﬁcients estimated from each ﬂat ﬁeld image acquired

by the same device is considered. As a result, it is not

necessary to adopt any denoising or averaging method

for K estimation.

The source identiﬁcation algorithm is then sket-

ched as below.

Let W be the image to be classiﬁed and let J

i,d

i = 1, ..., m the set of FF images acquired by the d-th

device.

1. For each device d

• compute the feature vector α

(α

R,i

, α

G,i

, α

B,i

) for each ﬂat ﬁeld image

i,d

by linear regression according to eq. (3),

where f is the diagonal of J

∗

i,d

domain

• set α

= (α

, α

), with α

∗

computed as in

eq. (4). α

is the reference feature vector for

the device d

2. Compute the feature vector α for the image W

3. For each device d, compute the distance D be-

tween α and α

, i.e.

D(α, α

) = kα − α

4. Assign the image W to the device

d realizing the

minimum distance value, i.e.

d = argmin

D(α, α

3 EXPERIMENTAL RESULTS

The proposed feature has been tested on the pub-

licly available Dresden database (Gloe and Bhme,

2010) that includes hundred images (natural and ﬂat

ﬁeld) captured by several camera models and devices.

For comparative studies, the method in (Lukas et al.,

2006) has been considered as the reference pioneering

one. The objective of the presented tests is to quantify

the ability of the proposed (single) feature in assign-

ing each image in the database to its source device.

In all tests W is a ﬂat ﬁeld image and all the ﬂat ﬁeld

images in the database have been considered in the

source identiﬁcation task. Hence, if W = J

i,d

, with

ﬁxed i, is the image to be classiﬁed, then it is com-

pared with all the devices in the database but the fea-

ture vector for the device d, i.e. α

, is estimated using

all the ﬂat ﬁeld images taken by d except for the one

assigned to W . In addition, the range of frequencies

used for Fourier spectrum decay has been empirically

set equal to 10% of the whole spectrum range.

Table 1 refers to results achieved on the whole

dataset, where the success rate is provided. The latter

is measured as the percentage of correct assignments

with respect to the number of considered candidate

images. As it can be observed, the success rate of the

proposed method is not negligible, especially if one

takes into account that just one global image feature

(one parameter for each color channel) has been used

in the matching phase. In fact, one of the main advan-

tage of the proposed approach is the use of a single

and easy to compute image feature in the identiﬁca-

tion process; the adopted feature is independent of

image size and spatial correspondences between the

two comparing images.

IMPROVE 2021 - International Conference on Image Processing and Vision Engineering

104

Table 1: Success rate provided by the proposed method on

Dresden database (ﬁrst column) and the ones provided by

the same method applied to the images partitioned into M

equally size subblocks.

Proposed Proposed Proposed

(M = 4) (M = 16)

Device 51.4 85.3 92.8

Model 64.6 92.9 96.9

Brand 67.2 94.7 98.1

In order to further evaluate the advantages and/or

limits of the proposed method, brand and model clas-

siﬁcation rates have also been considered. As it can be

observed in the same table, the success rate increases

as the reference set enlarges. This means that many of

the incorrect device assignments are within the same

device model or, more in general, within the same de-

vice brand. As a result, the proposed feature is able to

capture the characteristics of the ”device family”.

Table 1 also contains the results achieved by the

proposed method whenever images are partioned in

4 and 16, respectively, rectangular subregions hav-

ing the same size and the vector of coefﬁcients es-

timated in each subregion is used for classiﬁcation

purposes. This application mode allows for better

capturing some local image features. As it can be

observed, identiﬁcation success rate signiﬁcantly in-

creases thanks to the use of a more local information.

In order to perform comparative studies, the pro-

posed method using 16 sub-blocks has been consid-

ered and two different subsets of devices have been

extracted from Dresden database. The ﬁrst testing set

is composed of 23 devices (belonging to 7 brands)

whose ﬂat ﬁeld images have the same size (see Ta-

ble 2); the total number of images in this set is 950.

The second testing set is composed of 21 devices (be-

longing to 8 brands) whose ﬂat ﬁeld images can have

different dimension (see Table 3); the number of im-

ages in the whole subset is 900. For the second test-

ing set, the method in (Lukas et al., 2006) requires

cropping or subsampling in order to compare the nor-

malized correlation coefﬁcient. As Table 4 shows, al-

though the use of a single global feature, the proposed

method allows to reach moderately high success rates.

Even in this case, the success rate increases whenever

model and brand assignments are considered. The

same table contains the results achieved by the ref-

erence method in (Lukas et al., 2006) whenever the

denoising step is omitted in the estimation of device

reference PRNU. In this way the two methods have

comparable computational complexity. As it can be

observed, the proposed method achieves results that

are close to the basic version of the method in (Lukas

et al., 2006), i.e. 100%, but it outperforms it whenever

denoising is not applied. These results prove a cer-

Table 2: Testing set I: the images have the same size, i.e.

2736 × 3648. For each model, the number of devices and

the number of images for each device is provided.

Model

no. Devices no. Images

Olympus MJU 5 50

Pentax Optio A40 1 50

Samsung NV15 3 50

Sony Cyber-shot 4 50

DSC-T77

Sony Cyber-shot 2 50

DSC-W170

Panasonic Lumix 2 25

DMC-FZ50

Ricoh Caplio 5 25

GX100

Table 3: Testing set II: the images have different size.

Model Image size no. no.

Dev. Imgs

CanonIXUS55 1944 × 2592 1 50

CanonIXUS70 2304 × 3072 3 50

NikonS710 3264 × 4352 5 50

NikonD200 2592 × 3872 2 25

NikonD70 2000 × 3008 2 25

NikonD70S 2000 × 3008 2 25

SamsungL74 2304 × 3072 3 50

SamsungNV15 2736 × 3648 3 50

tain robustness of the proposed feature to background

noise.

4 CONCLUSIONS

In this paper a novel feature for PRNU image has been

proposed and its contribution to source camera iden-

tiﬁcation has been evaluated. It consists of the decay

of the Fourier spectrum of a particular sampling of a

sorted version of PRNU matrix. This decay is strictly

related to the regularity of the signal under study and

then it represents one of its representative features. As

the paper presented a feasibility study, ﬂat ﬁeld im-

Table 4: Success rate on two different testing sets: com-

parisons between the proposed method (Prop.) using image

partitioning into 16 subblocks and the method (Lukas et al.,

2006) (L06) when denoising ﬁlter is not applied before FF

averaging in the estimation of the reference pattern.

Testing set I Testing set II

Prop. L06 Prop. L06

Device 99.5 99,2 92.9 94.7

Model 99.9 99.9 92.9 99.9

Brand 99.9 99.9 92.9 99.9

A Novel Fourier-based Approach for Camera Identiﬁcation

105

ages have been considered. Preliminary and extensive

tests performed on a publicly available database have

shown that the proposed feature has some potential in

contributing to the solution of the source identiﬁca-

tion problem and it is able to reach high success rates

whenever properly estimated. On the other hand, it

has the advantage of being independent of image size,

so that artiﬁcial operations are useless whenever two

PRNU images have to be compared; ﬁnally, due to

its nature, it can show some robustness to background

noise sources. Future research will be then devoted to

reﬁne the proposed feature, making it able to capture

both global and local image characteristics; to extend

it to natural images and to evaluate its performance on

natural images and different datasets.

REFERENCES

Akshatha, K., A.K. Karunakar, H. A., Raghavendra, U., and

Shetty, D. (2016). Digital camera identiﬁcation using

prnu: A feature based approach, digital investigation.

In Digital Investigation.

Al-Ani, M. and Kheliﬁ, F. (2017). On the spn estimation in

image forensics: A systematic empirical evaluation.

In IEEE Trans. on Inf. Forensics and Security.

Caldelli, R., Amerini, I., and Tsun, L. C. (2018). Prnu-based

image classiﬁcation of origin social network with cnn.

In Proc. of EUSIPCO 2018.

Chen, M., Fridrich, J., Goljan, M., and Lukas, J. (2008).

Determining image origin and integrity using sensor

noise. In IEEE Trans. on Inf. Forensics and Security.

Chierchia, G., Parrilli, S., Poggi, G., Sansone, C., and Ver-

doliva, L. (2010). On the inﬂuence of denoising in

prnu based forgery detection. In Proc. of the 2nd ACM

workshop on Multimedia in forensics, security and in-

telligence.

Chierchia, G., Poggi, G., Sansone, C., and Verdoliva, L.

(2014). A bayesian-mrf approach for prnu-based im-

age forgery detection. In IEEE Trans. on Information

Forensics and Security.

Duff, G. F. D. (1967). Differences, derivatives, and decreas-

ing rearrangements. In Canadian Journal of Mathe-

matics.

Ferreira, P. (2001). Sorting continuous-time signals: Ana-

log median and median-type ﬁlters. In IEEE Trans. on

Signal Processing.

Fridrich, J. (2009). Digital image forensics. In IEEE Signal

Processing Magazine.

Georgievska, S., Bakhshi, R., Gavai, A., Sclocco, A., and

van Werkhoven, B. (2017). Clustering image noise

patterns by embedding and visualization for common

source camera detection. In Digital Investigation.

Gloe, T. and Bhme, R. (2010). The dresden image database

for benchmarking digital image forensics. In Journal

of Digital Forensic Practice.

Huang, Y., Zhang, J., and Huang, H. (2015). Camera model

identiﬁcation with unknown models. In IEEE Trans.

on Information Forensics and Security.

Korus, P. and Huang, J. (2016). Multi-scale analysis strate-

gies in prnu-based tampering localization. In IEEE

Trans. on Information Forensics and Security.

Kumar, B. V. K. V. and Hassebrook, L. (1990). Performance

measures for correlation ﬁlters. In Appl. Opt.

Li, R., Li, C. T., and Guan, Y. (2018). Inference of a com-

pact representation of sensor ﬁngerprint for source

camera identiﬁcation. In Pattern Recognition.

Lukas, J., Fridrich, J., and Goljan, M. (2006). Digital cam-

era identiﬁcation from sensor pattern noise. In IEEE

Trans. on Information Forensics and Security.

Mallat, S. (1998). A wavelet tour of signal processing. In

Academic Press.

Marra, F., Poggi, G., Sansone, C., and Verdoliva, L. (2017).

Blind prnu-based image clustering for source identiﬁ-

cation. In IEEE Trans. on Inf. For. and Sec.

Salvi, V. B. A. and Vitulano, D. (2019). Joint correlation

measurements for prnu-based source identiﬁcation. In

Lecture Notes in Computer Science, (Proc. of CAIP

2019).

Thaia, T. H., Retraintband, F., and Cogranne, R. (2015).

Camera model identiﬁcation based on the generalized

noise model in natural images. In Digital Signal Pro-

cessing.

Tiwari, M. and Gupta, B. (2018). Efﬁcient prnu extraction

using joint edge-preserving ﬁltering for source cam-

era identiﬁcation and veriﬁcation. In Proc. of IEEE

ASPCON 2018.

Valsesia, D., Coluccia, G., Bianchi, T., and Magli, E.

(2017). User authentication via prnu-based physical

unclonable functions. In IEEE Trans. on Information

Forensics and Security.

Xu, B., Wang, X., Zhou, X., Xi, J., and Wang, S. (2016).

Source camera identiﬁcation from image texture fea-

tures. In Neurocomputing.

Zhao, Y., Zheng, N., and T. Qiao, M. X. (2019). Source

camera identiﬁcation via low dimensional prnu fea-

tures. In Multimedia Tools and Applications.

IMPROVE 2021 - International Conference on Image Processing and Vision Engineering

106