基于3D洛伦兹的优化张量压缩感知图像的联合加密和压缩算法

Simultaneous encryption and compression of images based on optimized tensor compressed sensing with 3D Lorenz

目前图像的联合加密和压缩技术通常指有损压缩技术,但在大多数情况下由于其不适用于本质上由张量代表的3D医学图像,因此重建图像不能满足医学图像的精确度要求。基于此,提出一种基于张量的张量压缩感知(TCS)算法,通过该算法重建的图像可达到满足医学图像精确度的要求,解决传统联合压缩和加密算法存在的不足。采用交替最小二乘法并通过由离散3D洛伦兹加密的测量矩阵来进一步优化TCS,提高重构图像的解密精度。实验结果表明:提出的算法保留了基于张量的3D图像的内在结构,在相同压缩比下,解密精确度越高,提出算法的压缩性能越好,并实现了压缩比、解密精度和安全性之间更佳的平衡关系。此外,以张量积的特性作为附加密钥来增加未授权解密的难度。通过数值模拟实验结果可验证提出算法的有效性和可靠性。

The existing techniques for simultaneous encryption and compression of images refer lossy compression at present.Their reconstruction performances did not meet the accuracy of medical images because most of them have not been applicable to three-dimensional(3D)medical image volumes intrinsically represented by tensors.We propose a tensor-based algorithm using tensor compressive sensing(TCS)to address these issues.The image reconstructed by the algorithm can meet the requirements of medical image in the aspect of accuracy,and which solves the shortcomings of the traditional simultaneous encryption and compression algorithms.Alternating least squares is further used to optimize the TCS with measurement matrices encrypted by discrete 3D Lorenz,which improves the accuracy of the decrypted image reconstructed.The Experimental results show that the proposed method preserves the intrinsic structure of tensor-based 3D images.Under the conditions of same compression ratio,the higher the decryption accuracy,the better the compression performance of the proposed algorithm,and which achieves a better balance of compression ratio,decryption accuracy,and security.Furthermore,the characteristic of the tensor product can be used as additional keys to make unauthorized decryption harder when the attacker attempts to decrypt images.Numerical simulation results verify the validity and the reliability of this scheme.