$\ell_1$SABMIS: $\ell_1$-minimization and sparse approximation based blind multi-image steganography scheme

Steganography plays a vital role in achieving secret data security by embedding it into cover media. The cover media and the secret data can be text or multimedia, such as images, videos, etc. In this paper, we propose a novel $\ell_1$-minimization and sparse approximation based blind multi-image steganography scheme, termed $\ell_1$SABMIS. By using $\ell_1$SABMIS, multiple secret images can be hidden in a single cover image. In $\ell_1$SABMIS, we sampled cover image into four sub-images, sparsify each sub-image block-wise, and then obtain linear measurements. Next, we obtain DCT (Discrete Cosine Transform) coefficients of the secret images and then embed them into the cover image\textquotesingle s linear measurements. We perform experiments on several standard gray-scale images, and evaluate embedding capacity, PSNR (peak signal-to-noise ratio) value, mean SSIM (structural similarity) index, NCC (normalized cross-correlation) coefficient, NAE (normalized absolute error), and entropy. The value of these assessment metrics indicates that $\ell_1$SABMIS outperforms similar existing steganography schemes. That is, we successfully hide more than two secret images in a single cover image without degrading the cover image significantly. Also, the extracted secret images preserve good visual quality, and $\ell_1$SABMIS is resistant to steganographic attack.