Abstract
In recent years, driven by the development of steganalysis methods, steganographic algorithms have been evolved rapidly with the ultimate goal of an unbreakable embedding procedure, resulting in recent steganographic algorithms with minimum distortions, exemplified by the recent family of Modified Matrix Encoding (MME) algorithms, which has shown to be most difficult to be detected. In this paper we propose a compressed sensing based on approach for intrinsic steganalysis to detect MME stego messages. Compressed sensing is a recently proposed mathematical framework to represent an image (in general, a signal) using a sparse representation relative to an overcomplete dictionary by minimizing the l1-norm of resulting coefficients. Here we first learn a dictionary from a training set so that the performance will be optimized using the KSVD algorithm; since JPEG images are processed by 8x8 blocks, the training examples are 8x8 patches, rather than the entire images and this increases the generalization of compressed sensing. For each 8x8 block, we compute its sparse representation using OMP (orthogonal matching pursuit) algorithm. Using computed sparse representations, we train a support vector machine (SVM) to classify 8x8 blocks into stego and non-stego classes. Then given an input image, we first divide it into 8x8 blocks. For each 8x8 block, we compute its sparse representation and classify it using the trained SVM. After all the 8x8 blocks are classified, the entire image is classified based on the majority rule of 8x8 block classification results. This allows us to achieve a robust decision even when 8x8 blocks can be classified only with relatively low accuracy. We have tested the proposed algorithm on two datasets (Corel-1000 dataset and a remote sensing image dataset) and have achieved 100% accuracy on classifying images, even though the accuracy of classifying 8x8 blocks is only 80.89%.
Key Words— Compressed Sensing, Sparcity, Data Dictionary, Steganography, steganalysis