Natural Steganography in JPEG Domain with a Linear Development Pipeline

In order to achieve high practical security, Natural Steganography (NS) uses cover images captured at ISO sensitivity $ISO_{1}$ and generates stego images mimicking ISO sensitivity $ISO_{2}>ISO_{1}$. This is achieved by adding a stego signal to the cover that mimics the sensor photonic noise. This paper proposes an embedding mechanism to perform NS in the JPEG domain after linear developments by explicitly computing the correlations between DCT coefficients before quantization. In order to compute the covariance matrix of the photonic noise in the DCT domain, we first develop the matrix representation of demosaicking, luminance averaging, pixel section, and 2D-DCT. A detailed analysis of the resulting covariance matrix is done in order to explain the origins of the correlations between the coefficients of $3\times3$ DCT blocks. An embedding scheme is then presented that takes in order to take into account all the correlations. It employs 4 sub-lattices and 64 lattices per sub-lattices. The modification probabilities of each DCT coefficient are then derived by computing conditional probabilities from the multivariate Gaussian distribution using the Cholesky decomposition of the covariance matrix. This derivation is also used to compute the embedding capacity of each image. Using a specific database called E1 Base, we show that in the JPEG domain NS (J-Cov-NS) enables to achieve high capacity (more than 2 bits per non-zero AC DCT) and with high practical security ($P_{\mathrm{E}}\simeq40\%$ using DCTR from QF 75 to QF 100).