DeepELIC: Deep encrypted lossy image compression network via compressive sensing unfolding

Encrypted image compression plays an important role in data-sensitive areas, aiming to compress the encrypted image while ensuring its security. In this paper, we propose a novel deep Encrypted Image Compression network, namely DeepELIC, based on a compressive sensing (CS) unfolding strategy. Specifically, we first develop a CS-based Encrypted Image Compression (CS-EIC) algorithm that establishes a mathematical foundation for our network design. Then, we unfold the iterative solution of CS-EIC into a novel network DeepELIC. To the best of our knowledge, our work is the first successful endeavor to design a deep unfolding network for encrypted image compression, which fills the blank of this area. Compared to existing methods, our DeepELIC network has three main advantages. (1) Interpretable architecture: deriving from the unfolding strategy, the network maintains strict mathematical correspondence with the CS-EIC algorithm, with each module retaining good physical meanings; (2) Integrated reconstruction: different from recent learning-based lossy ETC methods, image decryption and decompression are jointly performed in our reconstruction process, to fully explore their correlations for improving reconstruction accuracy; (3) Superior performance: exhaustive evaluations on four datasets across various compression ratios demonstrate the network's exceptional compression performance on encrypted images. The software codes are available at https://github.com/Xiao-Fang-12138/DeepEIC_encrypted_image_compression.