A lossy compression scheme for encrypted images exploiting Cauchy distribution and weighted rate distortion optimization

How to improve the compression efficiency of encrypted signals remains a challenging problem. To alleviate this problem, this paper develops a new compression scheme on encrypted gray images by exploiting the Cauchy distribution and the weighted rate-distortion optimization (wRDO). In the scheme, the low-frequency and wavelet subbands generated through lifting wavelet transform are encrypted by stream and permutation ciphers, respectively. They are then compressed in lossless and lossy ways, respectively. Inverse operations are finally conducted at the receiver to reconstruct the original image. The lossy compression is formulated as a problem of wRDO and further solved by incorporating the Cauchy distribution that is demonstrated via extensive simulations to well characterize statistical distributions of wavelet subbands. Experimental results show that the proposed scheme is significantly better than other permutation-based prior arts and achieves comparable or even better performance in comparison to the conventional JPEG algorithm with original unencrypted images as input.