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Table 2 Notation

From: Detection of shifted double JPEG compression by an adaptive DCT coefficient model

 

Description

D, DO, DAJ, DSJ, DSD

DCT coefficients of an 8 × 8 image block, where the superscripts O, AJ, SJ, and SD stand for the original block before JPEG compression, the block after aligned JPEG compression, the block after shifted JPEG compression, and the block after shifted double JPEG compression respectively. Note that no superscript stands for the general case

D m , n O , D m , n AJ , D m , n SJ , D m , n SD

The (m,n)th DCT coefficient of an 8 × 8 image block, the subscript (m,n) stands for the (m,n)th DCT mode

E m , n AJ , E m , n SJ , E m , n SJR

Quantization error of the (m,n)th DCT coefficient caused by aligned JPEG compression, shifted JPEG compression, and shifted JPEG compression with spatial rounding, respectively

σ m , n SJ , σ m , n SJR

Standard deviation of the quantization error of the (m,n)th DCT coefficient caused by shifted JPEG compression and shifted JPEG compression with spatial rounding, respectively

hm,n(f), h m , n AJ f , h m , n SS f , h m , n SD f

Histograms of the (m,n)th DCT coefficient of the image patch, where the superscripts AJ, SS, and SD stand for the image patch after aligned JPEG compression, the SSJPEG patch and the SDJPEG patch, respectively. Note that no superscript stands for the general case

(xS, yS)

Coordinate shift of the shifted JPEG compression

QF1, QF2

Quality factor of the primary JPEG compression and the final JPEG compression, respectively

qm,n(QF)

Quantization step of the (m,n)th DCT mode with the quality factor QF.

G(μ, σ)

Gaussian distribution with mean μ and standard deviation σ