基于马尔科夫随机场的加密图像压缩与重构算法研究

How to achieve the efficient compression and high-quality reconstruction on encrypted signals is a fundamental problem with scientific significance and potential applications for cloud computing in the big-data era. Current researches on this topic mainly exploit statistic properties of cover media in the encryption (i.e., the cloud client) or compression (i.e., the cloud platform) side, which would either increase the computational burden on the encryption side or result in the statistical information leakage and thus would hinder its practical applications. Our preliminary research and analysis indicates that a more practical way for compression of encrypted signals is to fully exploit the statistic property of cover media at the receiver side that has sufficient computational capability and the encryption key. This motivates us to deploy the Markov random field (MRF) to characterize the spatial statistical distribution of cover image, represents the MRF with a factor graph by applying the theory of factor graph, and further integrates it with the factor graph of the low-density parity code (LDPC) decoding, which yields a graph model for image reconstruction. Through this line of thoughts, in this proposal we will exploit statistical characteristics of binary and grey images to construct several reconstruction graph models for lossless compression, in which two/multiple-state MRF and binary/n-ary LDPC are well integr-ated in an optimized manner. Furthermore, we will also extend our research to the case of color image and to the scenario of lossy compressi-on. It can be expected that the proposal would achieve higher compression ratios at the same reconstruction quality, and thus would well facilitate the development and application of cloud computing in the big-data era and reversible data hiding in the encrypted domain.

如何对加密信号进行有效压缩及高质量重构是大数据时代云计算环境下具有重要科学意义和潜在应用价值的问题。当前这方面的研究主要是在加密方（即云用户）或压缩方（即云端）以某种方式利用载体信号的统计特性，但这会增加加密方的计算复杂度或引起统计信息泄露而不利于实际应用。本项目前期研究与分析表明，更利于实际应用的重要方向是在拥有较好计算能力及加密密钥的接收方充分利用载体信号的统计特性。为此，本项目以马尔科夫随机场（MRF）表征图像空域统计分布，并运用因子图理论将其表达为因子图，进而在接收方与LDPC解码因子图有机结合而构造原始图像重构图模型。基于此，本项目拟利用二进制/灰度图像特点构造基于二/多符号MRF与二/多进制LDPC优化结合的多种无损压缩重构图模型，并进一步推广到彩色图像及有损压缩情形。本研究将能在同等重构质量时获得更高压缩率，因而将有利于大数据时代云计算以及加密域可逆信息隐藏的发展和应用。

本项目针对加密图像的高效压缩问题开展一系列研究，取得研究成果主要体现在六个方面：（1）通过对加密信号压缩框架及现有文献的梳理分析，指出在拥有解密密钥及相当计算能力的接收方充分利用载体的统计特性以提高加密信号压缩效率是一种更为可行和有效的策略；（2）基于上述的策略，用二符号马尔科夫随机场（MRF）表征二值图像的空域统计特性，运用因子图理论构造MRF因子图，并在构造流密码解密和LDPC解码因子图的基础上将它们无缝整合在一起而形成二值图像无损重构用联合因子图，进而推导适合该联合因子图的“和-积”算法，从而设计基于二符号MRF的加密二值图像无损重构算法，大幅提升了加密压缩效率。在此基础上，进一步设计了基于二符号MRF的加密二值图像有损压缩算法；（3）用二符号MRF表征灰度图像位平面内及位平面间的统计相关特性，提出了基于二符号MRF的加密灰度图像无损压缩算法，提升了加密压缩性能；（4）类似基于二符号MRF的加密二值图像无损压缩算法，利用多符号MRF和用多进制LDPC设计流密码加密的灰度图像压缩与重构算法；（5）结合流密码加密和均匀下抽样式的加密图像压缩，把利用解密后的加密压缩图像有损重构原图像的问题表征为一个类似超分辨率的最优化问题，提出了一种基于空间关注机制的残差密集网络的加密彩色图像有损压缩算法；（6）将基于本项目开展过程中对载体图像统计特性的理解和认识拓展应用到可逆水印领域，提出了基于LASSO、预测块大小内容自适应、分部加权预测和水印嵌入模拟等预测器及相应的可逆水印算法，并提出了一种改进的多直方图可逆水印算法。..本项目的研究成果丰富和发展了加密图像压缩方面的研究，提升了加密图像有/无损压缩的性能，揭示了在拥有解密密钥及相当计算力的接收方充分利用载体统计特性以提升加密压缩效率的可行性及有效性。此外，本项目对图像统计特性的理解和认识亦拓展运用到可逆水印领域而丰富了该领域的研究。