A New Encryption-Then-Compression Scheme on Gray Images Using the Markov Random Field

Compressing encrypted images remains a challenge. As illustrated in our previous work on compression of encrypted binary images, it is preferable to exploit statistical characteristics at the receiver. Through this line, we characterize statistical correlations between adjacent bitplanes of a gray image with the Markov random field (MRF), represent it with a factor graph, and integrate the constructed MRF factor graph in that for binary image reconstruction, which gives rise to a joint factor graph for gray images reconstruction (JFGIR). By exploiting the JFGIR at the receiver to facilitate the reconstruction of the original bitplanes and deriving theoretically the sum-product algorithm (SPA) adapted to the JFGIR, a novel MRF-based encryption-then-compression (ETC) scheme is thus proposed. After preferable universal parameters of the MRF between adjacent bitplanes are sought via a numerical manner, extensive experimental simulations are then carried out to show that the proposed scheme successfully compresses the first 3 and 4 most significant bitplanes (MSBs) for most test gray images and the others with a large portion of smooth area, respectively. Thus, the proposed scheme achieves significant improvement against the state-of-the-art leveraging the 2-D Markov source model at the receiver and is comparable or somewhat inferior to that using the resolution-progressive strategy in recovery.