Identifying the Digital Camera from Natural Images Using Residual Noise and the Jensen–Shannon Divergence

Regarding the problem of digital camera identification, many methods have been proposed, and for several of them, their effectiveness has been verified on the basis of disputed flat images. However, in real cases the disputed images are natural images, rather than flat images. In that case, several of the already proposed methods are not effective. Hence, in this paper, a method is proposed for the digital camera identification from natural images based on the statistical comparison between the residual noise in the natural disputed images and the fingerprint defined for the eligible digital cameras. In the reported case studies, the HDR database provided by the Communications and Signal Processing Laboratory of University of Florence is used to select a set of eligible digital cameras, and from this image database, for each digital camera, a set of disputed flat images, a set of disputed natural images, and a set of flat reference images were selected. Thus, the fingerprint of each digital camera was calculated from the probability density function (PDF) of the photo-response nonuniformity (PRNU) extracted from its reference images. Therefore, in order to identify the source digital camera of a natural disputed image, the Jensen–Shannon divergence (JSD) was implemented to statistically compare the PRNU-based fingerprint of each eligible source camera against the noise residual of that disputed image. The proposed method has a similar effectiveness to methods based on the peak-to-correlation energy or the Kullback–Leibler divergence when the disputed images are flat images and the PRNU is considered, but it is significantly more effective than those methods when the disputed images are natural images.


Introduction
In order to use digital images as relevant artifacts in trials, some of the following three aspects should be guaranteed: (i) image discernment-determining whether an image represents a real event or it is a computer-generated image; (ii) image integrity-identifying modi cations in a digital image; and (iii) source camera identi cation-identifying the source camera of a digital image in order to match that camera to a speci c person [1][2][3]. If any of these three aspects is accomplished using e ective techniques, a digital image could have a high impact on legal civil, medical, administrative, or criminal investigations. In these three analysis approaches, the intrinsic noise extracted from the digital images can be harnessed.
Regarding image discernment, some works can be mentioned. For example, in 2008, Swaminathan et al. extracted traces from digital images due to processing operations performed on the digital cameras in order to determine whether a digital image was a camera output and it was possibly generated by other image production processes [4]. Also, in 2017, Chen et al. proposed a method to detect whether an image's source camera was antiforensically falsi ed, which is based on the characterization of di erent content-independent local pixel relationships introduced by demosaicing algorithms and antiforensic attacks [5]. In 2019, Long et al., considering that the PRNU is a unique attribute of natural images, used binary similarity measures of the PRNU to represent the differences between natural images and computer-generated images [6]. For this purpose, they used a library for support vector machines (SVM) and calculated the binary Kullback-Leibler distance, binary minimum histogram distance, binary absolute histogram distance, and binary mutual entropy from the PRNU in three-color channels (RGB) of digital images. In 2021, Long et al. proposed a robust method against postprocessing operations that, based on a convolutional neural network (CNN), discriminates natural images from computer-generated ones [7].
Regarding image integrity, the proposed methods have been designed to detect three manipulation types in digital images: splicing that consists of copying one or several regions of an image and pasting them into another digital image [8]; copy-move that refers to reproduce a portion of a digital image to another location within the same image [9]; and removal that refers to the fact some parts of the digital image are replaced to remove or hide objects [10].
Concerning the source camera identification, some works can also be mentioned. For example, in 2008, Bayram et al. used the detection of demosaicing traces to identify the source camera model of digital images [11]. Also, in 2016, Xu et al. used the image texture features extracted from wellselected color model and color channel to match the source digital cameras to their disputed digital images [12]. In that case, they considered as a working premise that digital content in an image is a silent witness. In 2017, Roy et al. proposed a methodology based on the extraction of the discrete cosine transform residual (DCTR) features to identify the source digital cameras for digital images [13]. ey used artificial neural networks considering particularly a combination of the random forest-based ensemble classification and the dimensionality of the principal component analysis (PCA) to improve the classification effectiveness. Also, in 2017 Qiao et al. proposed a noise model that depends on the statistical distribution of pixel intensity in JPEG images [14]. at model showed that nonlinear response of image pixels can be captured by characterizing the linear relation because those heteroscedastic parameters are used to identify the source camera device. In 2018, Gupta et al., considering that the existing methods of the PRNU extraction contain fine details of the image, proposed a preprocessing step applied to widely accepted PRNU extraction methods to separately consider the low-and highfrequency components of digital images [15]. In 2020, Cozzolino et al. proposed to leverage the image noiseprint to boost the performance of PRNU-based analyses [16]. ey consider as a fundamental premise that the noiseprint is a camera model fingerprint effective for several forensic tasks. In 2021, Quintanar-Reséndiz et al. proposed a forensic algorithm based on the Kullback-Leibler divergence when identifying source digital cameras for digital images; they proposed a device statistical fingerprint and image noiseprint based on the PDF of the PRNU extracted from flat digital images [17]. On the contrary, in 2020, Taspinar et al. investigated about source camera identification considering that digital images may have been captured using different resolutions and aspect ratios [18]. In 2021, Bennabhaktula et al. proposed a CNN-based method for capture device identification, which extracts from natural images homogeneous regions with very little scene information [19]. Most recently, in 2022, Xiao et al. reported a PRNU extraction method that, based on a densely connected hierarchical denoising network (DHDN), allows to identify the source capture devices (digital cameras or smartphone) for natural digital images, which were obtained from the Dresden and Daxing databases [20].
Accordingly, this work offers a solution to the problem of matching a digital camera (source camera) to a digital image (disputed image) and therefore having findings matching a source camera to a person. Recently, some studies have been reported about forensic methods related to the matching of source digital cameras to disputed digital images. e PRNU-based methods use correlation measures such as cross-correlation, peak-to-correlation energy, and correlation predictors [21], or they use filtering techniques [22] that use artificial neural networks and some artifacts introduced into digital images by the JPEG compression [13,23]. ere are several methods that verify their effectiveness by considering that the disputed images are flat images. For example, in 2021, Albisani et al. proposed a method that in addition to identifying devices leading to false attribution by the presence of NUAs (not unique artifacts), it also offers a solution of matching source digital cameras to flat disputed images [24]. Also, in 2021, Quintanar-Reséndiz et al. proposed a method to capture device identification from digital images when the disputed images were flat images [17]. However, this condition has no meaning in practice since the disputed images in a real case are natural images. erefore, a PRNU-based forensic method has been developed to identify the source camera for a digital image using a comparing strategy that applies the JSD to the PRNU-based statistical fingerprint extracted from each eligible source camera and the PDF computed for the PRNUbased residual noise extracted from a disputed image. Each PRNU-based statistical fingerprint for a source camera is computed by averaging the PDF of the PRNU extracted from the reference images shot using that eligible source camera, assuming that the PRNU of each digital image was extracted using the algorithm proposed in 2009 by Goljan et al. [25]. In contrast to other works based on peak-to-correlation energy (PCE) ratio [25] or normalized cross-correlation (NCC) [26] to identify a source digital camera for some disputed images, in this work, a statistical criterion based on JSD and PRNU signals was used. In order to show the effectiveness of the proposed method, two case studies were prepared from a set of digital images obtained from the HDR database provided in 2018 by Shaya et al. [27], which is available at https://lesc. dinfo.unifi.it/en/datasets. In both case studies, the PRNUbased statistical fingerprint for each eligible digital camera was created with flat reference images. Yet, in the first case study, the disputed images were flat images, and in the second case study, the disputed images were natural images. e main motivation for using the JSD is that it allows discrimination between two PDFs using entropy distances, and the underlying function does not suffer indeterminacy as in the Kullback-Leibler divergence (KLD) [28]. In this way, the JSD can be considered as an improved version of the KLD, which should be carefully coded in software implementations because it may cause indeterminacies.
us, this paper is organized as follows: in the Materials and Methods section, based on the noise model used by Chen et al. [22] and Python-implemented PRNU extractor on digital images [25], a description is given to estimate the camera fingerprint and the JSD is presented as a tool to statistically discriminate the source digital camera from disputed digital images; in the Results and Discussion section, the proposed method is presented and applied considering two case studies, one of them when the disputed images are flat images and the other one when they are natural images. In this section, the effectiveness of the proposed method is also evaluated. At the end of this section, some improvement alternatives are presented for the proposed method that can correctly identify a camera from natural disputed images; and finally, in the Conclusion section, the conclusions of this study are drawn.

Materials and Methods
As a preliminary remark, it is considered that a natural digital image contains edges, contrasts, and textures. Nonsmoothed image regions have texture changes and high contrast, and then, they have a high variance in the pixel intensities; yet, the smoothed image regions, lacking scene information, have low variance in pixel intensities. erefore, it is expected that the smoothed image regions facilitate the extraction of intrinsic signals such as the PRNU, because they include a significant noise content without scene information and the pixel intensities are not saturated; that is, the pixels are neither completely white (pixel at 255) nor black (pixel at 0) pixels. In addition, according to Fernández-Meduina and Pérez-González, the PRNU can be considered a zero-mean white Gaussian process with variance σ 2 k , independently of its spatial distribution on the image [29].
us, to define a PRNU-based statistical fingerprint for each eligible digital camera, firstly, it is assumed that there are different types of intrinsic signals in digital images: spatial noise, system noise, and temporal noise [17]. Spatial noise describes the variations of the intensities of different pixels due to the illumination considering homogeneous light. is noise is commonly named "sensor pattern noise" (SPN) because it is related to the sensor pattern of the digital camera. SPN can be identified as a signal whose spatially distributed intensity is maintained for different images captured for the same scene. SPN includes the PRNU, which quantifies image errors due to sensor imperfections. us, the PRNU contains unique features of digital camera sensor, and consequently, it is different for each digital camera. In this way, the PRNU can be considered to create the fingerprint of the digital camera sensors. On the contrary, system noise includes three noise sources: quantization noise produced by the analog-to-digital conversion required for the forming of each pixel in a digital image, lens defect noise produced by the manufacturing defects in the digital camera lens [30,31], and data processing noise due to the demosaicing process of the digital camera. Finally, temporal noise is produced by different sources such as photon, dark current, and readout [32]. is noise can be considered the dominant source of noise in a digital camera, and it is produced by the charge-coupled device (CCD).

Noise Model.
In this work, it is considered that the intrinsic signals of a digital image are generated by the source digital camera following the noise model defined by the following equation, which includes the additive and multiplicative noise components and is congruent with the noise model proposed in 2007 by Chen et al. [33]: where I is the noisy image, I 0 is the noise-free image, η is the multiplicative noise component, and δ is the additive noise component on the digital image. Solving (1) for η, the following equation is obtained: Now, if the noise-free image I 0 is estimated using a denoising filter, D(·), then I 0 ≃D(I) and a residual noise image I η can be obtained, which is influenced by η according to the following equation: us, according to Goljan et al. [25], δ can be eliminated in I η applying a Wiener filtering, W(·); that is, erefore, an approximation to the residual noise η is obtained according to the following equation: In this work, it is considered that the PRNU is represented by W(I η ). Yet, for the purpose of avoiding the influence of the image scene in the intrinsic traces of interest, η is used in all calculations. erefore, in the method proposed by Goljan et al. [25], the PRNU is extracted from a digital image according to the maximum-likelihood criterion and two PRNUs are compared using the PCE.
is PRNU extractor is based on the method proposed in 2009 by Goljan et al. [25] using a two-dimensional discrete wavelet decomposition attenuating the saturated pixels and normalizing the noise pattern to erase linear patterns. Note that it includes a Wiener filter to remove artifacts due to Journal of Electrical and Computer Engineering 3 JPEG compression. It is worth noting that although the work published in 2019 by Matthews et al. [36] considers other elements (lens artifacts or those produced by temperature) that could influence the identification process of source digital camera, similar to Goljan et al. [21], those elements were not considered. is decision was based in the fact that in 2014, Gisolf et al. [37] assured that the method proposed by Goljan et al. [21] was computationally slow compared with their method, but conversely, it was more accurate. us, in this work, accuracy is more important than the speed of the proposed method, and therefore, Goljan's method was used considering the version developed by Bondi and Bonettini [34]. In this way, the Python-implemented PRNU extractor v.1.2 is implemented in congruence with the MATLAB-implemented PRNU extractor by Binghamton University (https://dde.binghamton.edu/ download/camera_fingerprint); it processes digital images faster than the MATLAB-implemented PRNU extractor, and it has an open-source MIT License (see https://github. com/polimi-ispl/prnu-python/blob/master/LICENSE.md) [34].
In particular, for the Python-implemented PRNU extractor v.1.2 [34,35], the following parameter settings were used: wavelet decomposition levels, 4, sigma, which is related to the estimated noise power, 5; and wdft, sigma, which is related to estimated DFT (discrete Fourier transform) noise power, 0. As an example of the use of this algorithm, Figure 1(a) shows a flat digital image of 4160 × 3120 pixels captured by the digital camera in a smartphone Huawei P8, and Figure 1

PRNU-Based Statistical Fingerprint for Digital Cameras.
e PRNU-based statistical fingerprint for each eligible digital camera is estimated according to the following equation, which calculates the average of the PDFs of the PRNU extracted from the set of reference digital images of each digital camera: In the above formula, S is the number of reference digital images of the eligible digital camera y∈ (1, C), R is the size of a regular partition in the definition interval for the PRNU extracted from each reference digital image x∈ (1, S), and μ i (S, y) is calculated in a similar way to Quintanar-Reséndiz et al. in 2021 [17] (see (7)), considering that ρ i (x, y) is defined by (8), similar to Quintanar-Reséndiz et al. in 2022 [38].
where Δ � (b − a/R), R i P Ai � 1, and a and b are the limits of the definition interval for the PRNU.
Note that ρ i (x, y) represents each component of the estimated PDF of the PRNU extracted from each reference digital image x∈ (1, S) of the respective digital camera y∈(1, C); P Ai is the number of times that each pixel (u, v) lies in the subinterval A i in the definition interval of the PRNU, i � 1, 2, 3, . . ., R; m and n are, respectively, the number of rows and columns of each digital image x∈(1, S); and B Ai (u, v) denotes the belonging function of each PRNU component to the subinterval A i as expressed in the following equation similar to [17]: In this way, ρ(x, y) represents the PDF for the PRNU extracted from the reference digital image x∈(1, S) of the digital camera y∈(1, C).

Jensen-Shannon Divergence.
ere are various approaches to perform a comparison of PDFs such as the φ-divergence [39], the Kullback-Leibler divergence [17,40,41], the Hellinger distance [40,42,43], the coefficient of determination (R 2 ) [44,45], the Jeffrey divergence [46,47], and the Jensen-Shannon divergence [28,48]. Yet, in this work, the JSD was considered to be applied in the proposed method. e JSD can be understood as an improved version of the KLD, assuming that the KLD is a nonsymmetric measure of similarity between PDFs, and it was proposed in 1951 by Kullback and Leibler when they published the scientific meaning of "information" related to Fisher's concept of a "sufficient statistic." e KLD has many properties, but when it is used to compare PDFs, caution must be taken when coding a software implementation because it can cause indeterminacies when either distribution is zero. is is the main reason why the JSD was selected for this work. Now, according to Quintanar-Reséndiz et al. in 2021 [17], the KLD can be defined by equation (10) and it measures how one probability distribution D diverges from a second expected probability distribution μ(S, y). Note that the KLD achieves the minimum zero when D � μ(S, y) everywhere, and if D or μ(S, y) is zero, then the following equation generates computing errors: In this case, it is considered that D corresponds to the PDF of the residual noise extracted from a disputed image and μ(S, y) corresponds to the PRNU-based statistical fingerprint of eligible digital camera y considering S reference digital images.
On the contrary, the JSD is another measure of similarity between the two PDFs defined in [0, 1] according to Majtey et al. [28] by equations (11) and (12), and in contrast to the KLD, it is a symmetric function that can be considered a smoothed version of the KLD. where e KLD is a good tool for comparing two PDFs, as demonstrated by Vázquez-Medina in [49], and it represents the information lost, when μ(S, y) is used to approximate D; yet, it can cause computing errors caused by zero divisions. In contrast, the JSD is a smoothed and normalized version of the KLD, and it can be applied without computing errors. Furthermore, it has scores JSD � 0 when the PDFs under comparison are identical, and JSD � 1 when the PDFs under comparison are maximally different. Additionally, note that the JSD is always a non-negative function that can be equal to zero if and only if the two PDFs under comparison are identical.

Proposed Method.
e proposed method has been implemented to identify the source digital camera for disputed digital images using a statistical comparison strategy that applies the JSD. For this purpose, a set of C eligible digital cameras were used, and digital images were selected from the HDR database provided by Shaya et al. [27] (see https://lesc.dinfo.unifi.it/en/datasets). e proposed method consists of the following three steps: (1) Estimating the PRNU-based camera statistical fingerprint. For each digital camera, the PDF of the PRNU extracted from the S � 20 reference digital images is averaged. e PRNU is extracted from each full reference image and not from any segment of it.
(2) Estimating the residual noise PDF of disputed images. e PDF was calculated for the PRNU extracted from each full disputed image or from a set of selected pixels considering a low-contrast criterion.
(3) Comparing PDFs. e residual noise PDF from each disputed image is compared with the PRNU-based camera statistical fingerprints of C eligible digital cameras. e comparison strategy is based on the JSD considering that the smallest value of the JSD obtained will reveal the source digital camera for that disputed digital image. Unlike the method proposed by Quintanar-Reséndiz et al. [17], in which the PRNU was extracted from a clipping of each digital image, in this work the PRNU was extracted considering the full digital image in all cases. It is important to emphasize that, for disputed images, an additional step was included and explored in order to extract the PRNU from a set of selected pixels for each digital image instead of extract to it from an image clipping. us, in order to obtain the residual noise of a digital image, a pixel is selected for the PRNU extraction if its intensity corresponds to the average intensity obtained from the pixels used to estimate the fingerprint of each eligible digital camera considering the three criteria defined in the section named "Improvement Alternatives of the Proposed Method" of this work. Figure 2 shows the flowchart of the proposed method assuming that δ is used to select image pixels when their intensity is in (µ I -δ, µ I + δ), where µ I is the average pixel intensity obtained from the pixel intensities of all reference images used to obtain the PRNU-based statistical fingerprint, and δ is a tolerable deviation from µ I defined according to the following criteria.

Case Studies.
In order to show the effectiveness of the proposed method, two case studies were defined to identify the source digital camera that captured each disputed digital image. In the first case study, thirteen eligible digital cameras (C � 13) were used, and for each one of them, twenty flat images were used as reference digital images (S � 20) and twenty flat images as disputed digital images. en, two hundred and sixty reference digital images and two hundred and sixty disputed digital images were used. As an example of the flat disputed images used for this case study, Figure 3 includes images of the digital cameras in the smartphones Huawei Mate 10 Pro, OnePlus 3T, and iPhone 7.
On the contrary, for the second case study, thirteen eligible digital cameras (C � 13) were also used, and for each one of them, twenty flat images as reference digital images (S � 13) and twenty natural images as disputed digital images were used. en, two hundred and sixty reference images (flat images) and two hundred and sixty disputed images (natural images) were also used. As an example, Figure 4 shows natural disputed images used for this case study corresponding to images of the digital cameras in the smartphones Galaxy S7 (1), Xiaomi 3, and iPad Air.
It is important to emphasize that for both case studies, the digital images were downloaded from the HDR database provided in 2018 by Shaya et al. [27] and available at https:// lesc.dinfo.unifi.it/en/datasets by the Communications and Signal Processing Laboratory of University of Florence in Italy.
For the HDR database, the features of each digital camera are described in Table 1. It is worth noting that, in order to verify the robustness of the proposed method, two pairs of digital cameras with the same brand and model (Huawei Honor 6 Plus and Galaxy S7) were used. Additionally, note that the digital images of the digital camera from the smartphone Galaxy S7 have different resolutions.
at is, Galaxy S7 (1) has a resolution of 4032 × 3024; meanwhile, Galaxy S7 (2) has a resolution of 4032 × 22608. In this way, in congruence to the method proposed by Quintanar-Reséndiz et al. [17] and to make a fair comparison, twenty reference digital images (S � 20) were used considering a regular partition with R � 256 subintervals for the definition interval. Now, it is worth noting that the PRNU-based statistical fingerprint, μ i (S, y), for the eligible digital camera y was computed by the average of the PDFs estimated of the PRNU extracted from S reference digital images of each one of the C eligible digital cameras.

Discrimination Process Baseline.
In order to obtain a comparison baseline for the effectiveness of the proposed method, the method proposed by Quintanar-Reséndiz et al. [17] was applied when two cases were considered. Table 2 includes the summary of the effectiveness results for the method proposed by Quintanar-Reséndiz et al. [17] when the disputed images were flat images. Meanwhile, Table 3 includes the summary of its effectiveness results when the disputed images were natural images. In both experiments, the effectiveness of the aforementioned method was calculated from the number of times that for a disputed image the method resulted in the smallest JSD value for a specific digital camera divided by the number of eligible digital cameras. Additionally, when the method proposed by Quintanar-Reséndiz et al. [17] was used, the following parameters were considered for the PRNU extractor proposed by Goljan et al. [25]: wavelet decomposition levels, 4, sigma, which is related to the estimated noise power, 5; and wdft, sigma, which is related to estimated DFT noise power, 0. It is worth noting that the method proposed by Quintanar-Reséndiz et al. [17] processed image clippings from the digital images. ese image clippings were of size 500 × 500 pixels obtained from the image center. Yet, in this case study, the full digital images were used. Note that when the first case study was considered, the method proposed by Quintanar-Reséndiz et al. [17] had an effectiveness of 0.869 (see Table 2); meanwhile, when the second case study was considered, its effectiveness was of 0.007 (see Table 3). For both experiments, full digital images were considered. In both tables, the green cells indicate by row the highest effectiveness achieved for the method for each disputed image considering all eligible cameras. Meanwhile, the red boxes indicate by row the place where, in the ideal case, the highest effectiveness of the method should have been reached. In addition, the gray cells indicate by row the case with some effectiveness level achieved for the method for each disputed images considering other digital cameras but when the JSD did not reach the highest value.
It should be noted in Table 3, that the method proposed by Quintanar-Resendiz et al. [17] had many confusions when the analyzed disputed image was captured with the digital camera in the smartphone Xiaomi 3. In this case, the mentioned method produced co.
It should be noted in Table 3 that the method proposed by Quintanar-Reséndiz et al. [17] had many confusions when the analyzed disputed image was captured with the digital camera in the smartphone Xiaomi 3. In this case, the mentioned method produced coincidence in seven of thirteen digital cameras. Additionally, this method produced critical confusions when the analyzed disputed image was captured with the digital camera in the smartphone Huawei P8; in this case, the method produced coincidence in four of thirteen digital cameras.
Also, it should be noted in Table 3 that the method proposed by Quintanar-Reséndiz et al. [17] had many confusions in the association of a disputed image with its source digital camera. is can be noticed by the fact that there are many gray cells in Table 3, and in any case, the green cells are not on the table diagonal. At this point, it can be observed that the method proposed by Quintanar-Reséndiz et al. [17] has an acceptable effectiveness when the images in dispute are flat images, but it has a poor effectiveness when the images in dispute are natural images.
It is worth noting that most of the authors have shown a comparable average effectiveness of their algorithms in identifying the source digital camera when the disputed images are flat images [24,50]. According to the results in   Journal of Electrical and Computer Engineering Table 3, the method proposed by Quintanar-Reséndiz et al. [17] has an unsatisfactory effectiveness for the identification of any digital camera when the disputed images are natural images.

Discrimination of Source Digital Cameras.
In order to identify the source digital camera for each disputed digital image, using the JSD, the PRNU-based statistical fingerprint of each eligible digital camera was compared against the PDF  of the residual noise for each disputed image. Table 4 shows a summary of the result effectiveness of the proposed method when it was applied to the first case study, that is, when the disputed images are flat images. In this case, it should be noted that full images were processed when the PRNU was extracted. Similar to Table 2, in Table 4, the highest average effectiveness degree for the proposed method from flat disputed images is highlighted in green. It should be noted that the proposed method offered an average effectiveness of 0.90. According to the results in Tables 2-4, it should be noted that the effectiveness (0.904) of the proposed method is higher than the effectiveness (0.869) of the method proposed by Quintanar-Reséndiz et al. [17], when both methods were applied to the case study with flat disputed images.
Considering the results in Tables 3-5 and similar to the method proposed by Quintanar-Reséndiz et al. [17], the proposed method has very low effectiveness (0.062) when natural images were considered as disputed images.
However, in the following subsection, some approaches are proposed to improve the effectiveness of the proposed method when natural disputed images are considered.

Improvement Alternatives of the Proposed Method
Considering the results obtained when both methods were applied to flat disputed images and based on the work presented by Gupta and Tiwari [15], a preprocessing step applied to the PRNU extraction was proposed in order to avoid the scene information from natural images. is approach to extract the PRNU considers only the image pixel similar to the pixel in smoothed image regions discussed in the Materials and Methods section.
us, in the preprocessing step, only the PRNU of a reduced set of image pixels inside the disputed natural images was considered. An image pixel can be selected only if its intensity is close to the average intensity obtained from the pixel intensities of the Table 2: Effectiveness of the method proposed by Quintanar-Reséndiz et al. [17] when it is applied to the first case study (reference and disputed images are flat images). Digital cameras   HP8 HP10 HMP10  GS7-1  GS7-2  HRY6-1  HRY6-2  XM3 OP3T AZ2  IP7  IPA  IP6   HP8   HP10    reference flat images used to obtain the PRNU-based statistical fingerprint of each eligible digital camera. In the following, it can be shown that using this preprocessing step in the PRNU extraction from natural images, the effectiveness of the proposed method increased from 0.062 to 0.743 approximately considering three alternatives. erefore, three alternatives for the preprocessing step to the PRNU extraction were applied in order to select image pixels from natural disputed images. In general, an image pixel can be selected when its intensity is in (μ I −δ, μ I +δ), where μ I is the average pixel intensity obtained from the pixel intensities of all reference images used to obtain the PRNU-based statistical fingerprint, and δ is a tolerable deviation from μ I defined according to the following criteria:
(2) δ � σ 1 intensity levels, where σ 1 is the standard deviation for the intensities of digital pixel for the first reference flat image in each eligible digital camera.
Although any of the 20 reference images could have been used, for the alternative 2, it was decided to use the first reference image assuming that all of them have similar pixel intensities.
On the contrary, Tables 6 and 7 show respectively (δ � 8, δ � σ 1 , and δ � 2) the summary of the effectiveness results for the proposed method considering the three cases above mentioned. Similarly, in these tables, the highest effectiveness of the proposed method is highlighted in green, the red boxes indicate by row the place where, in the ideal case, the highest effectiveness of the method should have been reached, and the gray cells indicate by row the case where some effectiveness level was achieved by the method for each disputed image with other digital cameras. It is worth noting that for the experiment in Table 6, the effectiveness of the proposed method is 0.735; for the experiment in Table 7, it is 0.754; and for the experiment in Table 8, it is 0.739 approximately. Also, it should be noted that for three     experiments, the proposed method does not discriminate between cameras of the same make and model in the smartphones Huawei Honor 6 Plus (HRY6-1 and HRY6-2). Yet, it does discriminate between cameras of the same make and model in the smartphones Galaxy S7 (GS7-1 and GS7-2). From the new approach presented to extract the PRNU from digital images, it can be shown that the effectiveness of the proposed method has increased significantly when a natural disputed image is intended to match a source digital camera.
is new approach suggests that from a natural digital image, it is possible to produce an equivalent flat digital image. Note that this equivalent flat image does not include scene information existing in the natural digital image. It must be remembered that scene information is highly contaminating and detrimental to the PRNU extracted from a natural digital image for the purpose of identifying its source digital camera.

Conclusions
In this work, a method for the identification of source digital cameras based on the PRNU is extracted from the digital images and the JSD was presented. In the proposed method, the PRNU-based statistical fingerprint of each eligible digital camera was estimated using the PDF of the PRNU extracted from twenty reference flat images. e proposed method discriminates the digital cameras by performing a statistical comparison applying the JSD between the PDF calculated from the residual noise extracted from a disputed digital image and the PRNU-based statistical fingerprint of each eligible digital camera. Two case studies were considered to show the effectiveness of the proposed method: (i) when flat images are used as disputed images, and (ii) when natural images are used as disputed images. e first version of the proposed method was shown to have low effectiveness (0.062) when the disputed images are natural images. Yet, when the PRNU was extracted from selected image pixels, the proposed method improved its effectiveness for the identification of source digital cameras of natural digital images achieving an effectiveness of 0.743 approximately. In all performed experiments, the effectiveness of the proposed method was estimated considering two hundred and sixty reference images to calculate the PRNU-based statistical fingerprint for each one of thirteen eligible digital cameras and two hundred and sixty disputed images shot by each eligible digital camera. In the first case study, only flat images as disputed images were used. Yet, in the second case, only natural images as disputed images were used. e case studies contained in this work were prepared from digital images downloaded from the HDR database provided at https://lesc.dinfo.unifi.it/en/datasets by the Communications and Signal Processing Laboratory of University of Florence. is work gives us a broader vision of the use of the divergence applied to PRNU-based statistical fingerprints of the digital cameras against the PRNU-based statistical noiseprint of the disputed images (flat or natural).