Compression Of Encrypted Images Exploiting Statistical Models

To protect data and the related privacy information,encrypted algorithms are usually used to encrypt the original data.The encryption operation,however,would limit further processing of the data.To solve this problem,more and more researchers explore the field of signal processing in the encrypted domain.Compression of encrypted signals is one of key problems in the field of encrypted signal processing,which addresses the encryption-then-compression(ETC)problem in the service-oriented scenarios like distributed processing,cloud computation,etc.In these scenarios,the content owner merely encrypts its signal and then sends it to the service provider like cloud platform because of limited computational resources.The service provider then compresses,without access to the encryption key,encrypted signals for saving bandwidth and storage space and then sends them to the receiver to decompress and decrypt.Due to the randomness of the encrypted carrier signal,the service provider cannot make full use of statistical characteristics of the carrier signal,as usually done in the traditional compression-then-compression situation.This thus turns the compression of encrypted signals into a challenge.To this end,this thesis uses statistical models in the receiver and the service provider to carry out the research of lossless and lossy compression of encrypted gray images,respectively.The previous work in our research group shows that it is preferable to use statistical characteristics of the carrier in the receiver with both feasible computing resource and the encryption key.Based on this,this work proposes a new compression scheme of encrypted binary images using the Markov random field(MRF).By extending this work to gray images,this thesis proposes a new compression scheme on encrypted gray images exploiting the MRF.In particular,this paper employs the MRF to characterize the statistical correlation between adjacent bit-planes of a gray image,represents it with a factor graph,and finally integrates it in the reconstruction factor graph within a bit-plane to construct a joint factor graph for the reconstruction of a gray image(JFGIR).Next,we further derive the sum-product algorithm(SPA)adapted to the JFGIR.In more detail,the original gray image is first divided into 8 bit-planes,and each bit-plane is then encrypted through a stream cipher.Each encrypted bit-plane is further compressed via the LDPC and transmitted to the receiver.The JFGIR and the corresponding SPA are finally applied to reconstruct the original gray image.Simulation results show that the proposed scheme achieves higher compression efficiency under perfect reconstruction,and it has better performance than the state of the art.Regarding the lossy compression,this thesis develops a new ETC scheme exploiting the Cauchy distribution and the rate-distortion optimization.In this scheme,the coarsest subband and the other wavelet subbands generated by lifting wavelet decomposition of a gray image are encrypted by stream and permutation ciphers,respectively.They are then compressed in lossless and lossy ways at the service provider,respectively.The receiver finally performs the inverse operations to reconstruct the original image.In compression,the Cauchy distributions is employed to well characterize the statistical distribution of wavelet subbands,and the rate-distortion theory is applied to derive optimal quantization steps for lossy compression.Experimental results show that the proposed algorithm can obtain higher compression efficiency and reconstruction quality.Moreover,it is significantly better than other permutation-based prior arts and achieves comparable or even better performance in comparison to the conventional JPEG algorithm.