Efficient Compression Of Encrypted Binary Images Using The Markov Random Field

Similar to the conventional compression with the original,unencrypted image as input,the recently-emerged compression on encrypted images generally exploits statistical correlation of natural images to improve the compression efficiency.Most of these compression schemes in the literature leverage statistical correlation at the content owner side or in the service provider side,which would either increase the computational burden on the content owner side or disclose statistical distributions to service providers and thus would probably hinder their practical applications.Through analysis on properties of the compression system for encrypted data,this paper believe that it is more preferable to exploit statistical correlation of natural images at the receiver side with both encryption key and sufficient computational capability,which in turn would improve the compression efficiency while achieving low computational complexity and sufficient security for the content owner and the service provider.Motivated by this thinking,this paper use the Markov random field(MRF)to characterize binary images in the spatial domain and represent it with factor graph.The constructed MRF graph is further integrated seamlessly with the factor graph modified from the Tanner graph of the low-density parity check(LDPC)decoding,yielding a joint factor graph for image reconstruction.Based on this,this paper then develop a new compression scheme for encrypted binary images,which involves the stream-cipher-based encryption,the LDPC-based compression,and the factor-graph-based image reconstruction.Preferable parameters for the proposed scheme are first determined via a numeric way on a test image and then applied to other binary images.Extensive simulations show that significant improvements in terms of compression bit rate(bbp)over the state of the art are achieved,which are generally far below entropies of the original test binary images and thus demonstrate the feasibility and effectiveness of the proposed scheme.