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JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics The 1st ACM Workshop on Information Hiding and Multimedia Security Wei Fan *, , Kai Wang * , Fran cois Cayre * , and Zhang Xiong *

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JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics

The 1st ACM Workshop on Information Hiding and Multimedia Security

Wei Fan *,†, Kai Wang *, Fran¸ cois Cayre *, and Zhang Xiong †

* GIPSA-lab, France † Beihang University, P. R. China

18-06-2013

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

What is forensics/anti-forensics to JPEG compression?

Forensics

The technique detecting tampering in digital media

Anti-forensics

The technique misleading forensic analyses Question: Has it been previously JPEG compressed?

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 2 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

State-of-the-art

Standard JPEG compression Quantization table estimation JPEG blocking detection DCT histogram smoothing Median filtering based deblocking

+

TV-based detector Calibration-based detector

JPEG forensics JPEG anti-forensics Countering JPEG anti-forensics

process

−100 −80 −60 −40 −20 20 40 60 80 100 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 −100 −80 −60 −40 −20 20 40 60 80 100 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 DCT coefficient value DCT coefficient frequency
  • Z. Fan and R. L. De Queiroz, “Identification of bitmap compression history: JPEG detection and

quantizer estimation,” ITIP, 2003

  • M. Stamm et al., “Anti-forensics of JPEG compression,” ICASSP, 2010
  • M. Stamm et al., “Undetectable image tampering through JPEG compression anti-forensics,” ICIP, 2010
  • G. Valenzise et al., “Countering JPEG anti-forensics,” ICIP, 2011
  • S. Lai and R. B¨
  • hme, “Countering counter-forensics: the case of JPEG compression,” IH, 2011

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 3 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Our objective: performing better JPEG anti-forensics

  • Better undetectability when tested under current existing

JPEG forensic detectors

✓ Quantization table estimation based detector DFq ✓ JPEG blocking artifacts detector DFb ✓ Total variation based detector DV ✓ Calibration based detector DL

  • Higher image visual quality of processed images compared

with state-of-the-art methods

✓ FSq, JPEG image processed by DCT histogram smoothing ✓ FSqSb, JPEG image processed by DCT histogram smoothing followed by median filtering based deblocking

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 4 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

JPEG anti-forensic experiment setup

  • 1338 genuine, uncompressed images of size 512 × 384 from

UCID corpus (v2) are used for test

  • Without loss of generality, only the luminance component of

the image is considered

  • UCIDTest contains the first 1000 images, while UCIDTrain

contains the last 338 images

  • Each UCIDTest image I is compressed with a random quality

factor Q ∈ [30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90] to JPEG image J

  • All types of JPEG anti-forensic forgeries are created from J

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 5 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Quantization table estimation based detector

Tested on BOSSBase (v1.01), which consists of 10,000 genuine, uncompressed images of size 512 × 512

  • FFP : false positive rate
  • P3: the portion of 3 among all “non-1”/“non-undetermined”

estimated quantization table entries

Archive PF P (%) P3 01 18.70 1653/1959 = 84.38% 02 12.40 957/1118 = 85.60% 03 4.50 175/187 = 93.58% 04 5.70 111/125 = 88.80% 05 10.50 986/1141 = 86.42% 06 61.50 9243/11033 = 83.78% 07 17.50 1084/1155 = 93.85% 08 43.90 5655/6670 = 84.78% 09 33.20 5062/5895 = 85.87% 10 44.30 6780/7720 = 87.82% Average 25.22 87.49%

  • Tested on UCIDTest
  • PFP = 16/1000 = 1.6%
  • P3 = 15/16 = 94.74%

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 6 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Reliability analysis

−10 −8 −6 −4 −2 2 4 6 8 10 0.1 0.2 0.3 0.4 0.5 0.6 DCT coefficient value DCT coefficient frequency −50 −40 −30 −20 −10 10 20 30 40 50 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 DCT coefficient value DCT coefficient frequency

When does the detector pick 3 instead of 1 ?

The likelihood for q = 3: L(3) = p0 × N × w(0, 3) + (1 − p0) ×

number of blocks in estimation

  • N × w(1, 3)

an even function defined in the estimation

+N × log 3 The likelihood for q = 1: L(1) = N × w(0, 1) + N × log 1 L(3) > L(1), when:

percentage of coefficients which are integer multiples of 3

  • p0 > 67.28%

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 7 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

The other three forensic detectors

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

False positive rate True positive rate

DFb DV DL Random guess

FSq

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

False positive rate True positive rate

DFb DV DL Random guess

FSqSb

  • The cost for FSqSb: to lose 5.13 dB of PSNR value compared

to JPEG images on average

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 8 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Stamm et al.’s method (FSq)

The key assumption

The unquantized DCT coefficients follow the Laplacian distribution for AC components

−250 −200 −150 −100 −50 50 100 150 200 250 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 DCT coefficient value DCT coefficient frequency

  • riginal

−250 −200 −150 −100 −50 50 100 150 200 250 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 DCT coefficient value DCT coefficient frequency

FSq

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 9 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

The addition of the dithering signal

Strategy

Noise is added randomly without any consideration of the local information of the image in the spatial domain

  • riginal (log + scale)

FSq (log + scale)

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 10 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

JPEG image restoration

Why?

  • Improve the image quality for the further loss during the

forgery creation

  • Improve the accuracy of the DCT quantization noise

estimation using calibration

Assumptions

  • xq = x + nq: JPEG image xq is obtained by adding

spatial-domain quantization noise nq to the original image x

  • nq is a random quantity, nq and x are independent

MAP criterion

ˆ x = arg max

x

p(x|xq) = arg max

x

p(xq|x)p(x) = arg max

x

p(nq)p(x)

  • M. A. Robertson and R. L. Stevenson, “DCT quantization noise in compressed images,” ITCSVT, 2005

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 11 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Using the EPLL framework

By maximizing the EPLL (Expected Patch Log Likelihood), we expect to find ˆ x in which every patch is likely under the patch prior

  • The quantization noise model: 0-mean multivariate Gaussian
  • The patch prior model: GMM (Gaussian Mixture Model)
  • 64 kinds of patches according to their relative position w.r.t.

JPEG blocks

  • The learning of models is performed on UCIDTrain
  • D. Zoran and Y. Weiss, “From learning models of natural image patches to whole image restoration,”

ICCV, 2011 JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 12 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

JPEG image restoration

The minimization problem

ˆ x = arg min

x

{

regularization parameter

  • λ

2

64

  • k=1
  • Pi∈Sk

the k-th group of patch extracting matrices

(Pi(xq − x))t

covariance matrix for the k-th kind of patch

  • C−1

k Pi(xq − x)

−

  • i

log p(

the i-th overlapping patch

  • Pix)}
  • The problem is solved using an approximate MAP procedure

and a Quantization Constraint Set (QCS) projection

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 13 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

JPEG image restoration results (PSNR in dB)

JPEG image FoE-based Proposed Lena Q1 30.71 31.95 32.06 Q2 30.08 31.44 31.48 Q3 27.45 28.83 28.94 Peppers Q1 30.72 32.04 32.09 Q2 30.17 31.61 31.59 Q3 27.66 29.35 29.40 Barbara Q1 25.95 26.65 26.94 Q2 25.60 26.31 26.56 Q3 24.05 24.86 25.00 Baboon Q1 24.32 24.77 24.84 Q2 24.14 24.62 24.68 Q3 22.14 22.61 22.61

  • Very competitive, for very low-rate JPEG compression
  • Around ten times faster, although achieving slightly lower

PSNR gain, for high-rate JPEG compression

  • D. Sun and W.-K. Cham, “Postprocessing of low bit-rate block DCT coded images based on a fields of

experts prior,” ITIP, 2007 JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 14 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Example results

  • The image quality has been improved
  • The DCT histogram is partly smoothed

restored image

−250 −200 −150 −100 −50 50 100 150 200 250 0.05 0.1 0.15 0.2 0.25 DCT coefficient value DCT coefficient frequency

(2, 2)

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 15 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Non-parametric DCT quantization noise estimation

JPEG image J

  • rginal image I

JPEG compression (Q)

recovered image ˆ I

image restoration

calibrated image ˆ Ic

crop by 1 pixel (→ ↓)

JPEG image ˆ Jc

JPEG compression (Q) DCT coefficient subtraction

forgery FFq

DCT histogram smoothing

estimated quantization noise ˆ Nq

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 16 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Experimental results

  • Tested on UCIDTest
  • The difference between the two KL divergences (FSq and I
  • vs. FFq and I) over all subbands is 0.1262 on average with

standard deviation 0.0731 1 2 3 4 5 6 7 8 1 −0.022 0.019 0.045 0.070 0.094 0.123 0.142 0.115 2 0.014 0.051 0.065 0.067 0.073 0.126 0.112 0.070 3 0.057 0.060 0.067 0.073 0.088 0.116 0.134 0.065 4 0.059 0.064 0.068 0.065 0.092 0.168 0.166 0.086 5 0.076 0.068 0.081 0.100 0.111 0.234 0.243 0.140 6 0.085 0.080 0.100 0.102 0.141 0.228 0.286 0.218 7 0.141 0.119 0.139 0.172 0.231 0.293 0.295 0.248 8 0.137 0.157 0.164 0.192 0.209 0.217 0.241 0.243

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 17 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Example results

  • Extra unnatural noise has been introduced
  • The DCT histogram is explicitly smoothed

FFq

−250 −200 −150 −100 −50 50 100 150 200 250 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 DCT coefficient value DCT coefficient frequency

(2, 2)

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 18 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Improved JPEG anti-forensics

  • Remove introduced extra unnatural noise (DCT histogram

smoothing)

  • Add some terms for JPEG anti-forensic purposes

The cost function

f =

regularization parameter

  • λ

2 x − xq2 +

regularization parameter

  • α × ι(x)
  • TV of x

+

regularization parameter

  • β

28

  • k=1

7

  • c=0

| νk(

calibrated image by c pixels

  • xc )
  • variance of subband k

− ˆ σ2

k

  • estimated variance from FFq

| +

  • i

regularization parameter

  • γ

2 Pix − zi2 − log p(

auxiliary variable for “Half Quadratic Splitting”

  • zi )

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 19 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Detection reliability and image quality

DFb DV DL PSNR (dB) SSIM J 0.9999 0.9865 0.9889 35.1918 0.9862 FSq 0.9166 0.9949 0.9972 31.5105 0.9584 FSqSb −0.2052 0.6824 0.1889 30.0621 0.9427 F −0.0365 0.1814 0.0517 34.2652 0.9745

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

False positive rate True positive rate

DFb DV DL Random guess

  • PFP = 5/1000 = 0.5%
  • P3 = 4/5 = 80%
  • average detection reliability
  • f 6 potential detectors

(similar to DL) is −0.1285 with standard deviation 0.1983

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 20 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Example results (spatial domain)

I J FSq FSqSb F

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Example results (DCT domain)

DCT quantization noise (log + scale)

−250 −200 −150 −100 −50 50 100 150 200 250 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 DCT coefficient value DCT coefficient frequency

(2, 2)

−100 −80 −60 −40 −20 20 40 60 80 100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 DCT coefficient value DCT coefficient frequency

(1, 6)

−30 −20 −10 10 20 30 0.05 0.1 0.15 0.2 0.25 0.3 0.35 DCT coefficient value DCT coefficient frequency

(7, 4)

−7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 DCT coefficient value DCT coefficient frequency

(8, 8)

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Conclusions

  • The proposed JPEG anti-forensic method can fool existing

detectors, as well as achieve a higher visual quality of processed images

  • The DCT histogram is explicitly smoothed by the proposed

DCT quantization noise estimation

  • Further research shall be devoted to the improvement of the

restoration of the JPEG image

  • More powerful detectors might be built by future study of

natural image statistics

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 23 / 24

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Introduction Reliability of detectors DCT histogram smoothing Anti-forensics Conclusions

Thank you for your attention! Q & A

JPEG Anti-forensics Using Non-parametric DCT Quantization Noise Estimation and Natural Image Statistics 24 / 24