Image steganography based on sparse decomposition in wavelet space

Sparse decomposition of wavelet coefficients of cover image blocks for data hiding is addressed in this paper. By using the proposed algorithm, the embedded secret message can be reliably extracted without resorting to the original image. We use all four sub-images (LL, LH, HL and HH) of the 2D wavelet transform for data embedding without losing the image imperceptibility. An over-complete dictionary matrix is estimated by using the KSVD dictionary learning algorithm, and then the secret message bits are inserted in the sparse representation of the wavelet coefficients over the estimated dictionary. This is believed to be one of the first approaches to the image data hiding that uses the sparse decomposition. Our experimental results show that the proposed method is robust against cropping and noise addition attacks. It is also robust against the lower than 0.2 degree rotation attacks. The results also show it possesses resistance to high order statistics analysis.