An efficient matrix embedding technique by using submatrix transform for grayscale images

Matrix embedding (ME) is a high performance technique for steganography. Unlike optimal matrix embedding algorithms, which require maximum likelihood (ML) decoding to determine the minimum modified changes, this study proposes an adaptive suboptimal algorithm, called the submatrix transformation matrix embedding (STME) algorithm. The STME algorithm combines the original ME technique with adaptive techniques to improve embedding efficiency and complexity. Several concerns are related to cover location selection, such as the modification of less significant covers, changeable parts of the cover, and forced modification of the cover when embedding a secret message into the cover. The STME algorithm can embed q-ary message vectors at arbitrary specified cover locations. Consequently, the embedded message can be recovered at the receiver, without any damage to the associated cover locations. The simulation results indicate that the STME algorithm offers a trade-off between computational time complexity and embedding efficiency. Moreover, the experimental results show that the STME algorithm has the advantage of adaptive embedding, unlike conventional ME algorithms. The results also show efficiency difference between the optimal ME algorithm and the STME algorithm.