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Nowadays, it remains a major challenge to efficiently compress encrypted images. In this paper, we propose a novel encryption-then-compression (ETC) scheme to enhance the performance of lossy compression on encrypted gray images through heuristic optimization of bitplane allocation. Specifically, in compressing an encrypted image, we take a bitplane as a basic compression unit and formulate the lossy compression task as an optimization problem that maximizes the peak signal-to-noise ratio (PSNR) subject to a given compression ratio. We then develop a heuristic strategy of bitplane allocation to approximately solve this optimization problem, which leverages the asymmetric characteristics of different bitplanes. In particular, an encrypted image is divided into four sub-images. Among them, one sub-image is reserved, while the most significant bitplanes (MSBs) of the other sub-images are selected successively, and so are the second, third, etc., MSBs until a given compression ratio is met. As there exist clear statistical correlations within a bitplane and between adjacent bitplanes, where bitplane denotes those belonging to the first three MSBs, we further use the low-density parity-check (LDPC) code to compress these bitplanes according to the ETC framework. In reconstructing the original image, we first deploy the joint LDPC decoding, decryption, and Markov random field (MRF) exploitation to recover the chosen bitplanes belonging to the first three MSBs in a lossless way, and then apply content-adaptive interpolation to further obtain missing bitplanes and thus discarded pixels, which is symmetric to the encrypted image compression process. Experimental simulation results show that the proposed scheme achieves desirable visual quality of reconstructed images and remarkably outperforms the state-of-the-art ETC methods, which indicates the feasibility and effectiveness of the proposed scheme.

Enhancing Performance of Lossy Compression on Encrypted Gray Images through Heuristic Optimization of Bitplane Allocation