基于随机矩阵编码的数字密写研究

Designing steganographic schemes with embedding efficiency arbitrarily close to its upper bound and feasible computational complexity is still a challenging research problem leading to scientific significance and application value. In this investigation, we first utilize the random code with execellent asymptotical behavior for upper or lower bounds to construct the encoding matrix for steganography, and formularize, under the constraint of maximum number of allowing modified cover bits, the random-code-matrix-based steganography as the problem of sparse representation. Such formulation is then solved in feasible computational complexity by exploiting the theories and methods of sparse representation. We proceed to study the optimal construction of random-code-based encoding matrix and accordingly obtain a class of encoding matrix for any concerned combination of code length, sparity, and continuous relative embedding capcity.Via these encoding matrices, we aim to reveal the asymptotic approximation of the random-code-matrix-based steganographic schemes to the upper bound of embedding efficiency. Secondly, we design new distortion profiles and functions, attempting to well disclose the effectiveness of cover modifications in steganography on both local statistical characteristics and steganalysis and, thus, to better guide the steganographic algorithm to hide adaptively the message in the cover elements with least distortion and least detection of steganalysis. Finally, we further integrate the developed distortion profiles/functions into the proposed random-code-based matrix encoding to achieve a steganographic performance closer to the upper bound of embedding efficiency of steganography. To that end, we formularize the integrated system as an optimization problem of sparse representation and solve it with tolerable computational complexity in the framework of sparse representation. Such results are further exploited in our investigation to design new steganographic scheme that is more secure to steganalysis tools and applicable to practical situations.

如何以可行的计算复杂度获得任意逼近嵌入效率上界的矩阵编码密写算法是数.字密写领域具有重要科学意义和实用价值的问题。首先，本项目利用具有良好渐近最优性能的随机码设计矩阵编码，并在限定最大可修改比特数目的基础上将矩阵编码问题转化为稀疏表征问题，进而利用稀疏表征的相关理论和方法获得具有多项式计算复杂度的编码算法。进一步研究随机编码矩阵的最优构造方法，获得一簇针对任意载体长度、稀疏程度和连续嵌入容量的随机编码矩阵，并籍此揭示基于随机矩阵编码的密写方法对嵌入效率上界的逼近性能。其次，本项目设计失真原型和失真函数，以更好地反映载体元素的修改对局部统计特性及密写分析的影响，从而更好地引导密写算法自适应地将信息嵌入到失真最小、最不利于密写分析的载体元素中。最后，我们将失真原型/函数与随机矩阵编码进行整体优化，并研究具有多项式复杂度的优化求解方法，以更进一步逼近嵌入效率上界，进而设计更实用、安全的密写算法。

设计具有高效嵌入效率的矩阵编码以及构造能良好反映数字密写对统计特性影响的失真原型/函数，是提高数字密写性能的核心问题。本研究项目通过分析现代数字密写分析工具的特点以及数字密写对统计特征的影响特性，构造了两种自适应失真函数，能较好地引导STC将秘密信息嵌入到对统计特征影响较小的系数中，进而提升了数字密写的性能，与同类最好数字密写算法性能相当或更好。本研究项目将数字密写问题表征为矩阵编码问题，并利用稀疏矩阵理论和方法去构造具有高嵌入效率的随机编码矩阵。我们获得了相应的结果，不过在同等的计算复杂度情况下性能不如其他研究人员提出的、高性能的校正子网格编码（STC），影响了结果的实际应用价值。. 此外，我们尝试应用冗余小波分析数字密写对统计关系的变化时，利用数值分解方法和理论推导方法构造了两种具有可旋转、可缩放和平移不变性的可变形金字塔变换（DPT），发现并推导了旋转、缩放和平移的同步机制。虽然利用DPT没能更好地揭示数字密写对统计关系的变化，但鉴于其良好的几何同步特性，我们利用其设计了抵抗几何攻击的数字水印算法，取得了较好的抗几何攻击性能。我们亦尝试应用研究过程中累积的稀疏矩阵理论和方法对加密图像进行压缩，设计了两种加密图像压缩算法，所获得的性能优于同类最好加密图像压缩算法，且与针对未加密原图像的JPEG压缩性能相当甚至更好。