Three Dimensional Image Copression And Encryption Based On Tensor Compressive Sensing And Discrete Fractional Random Transform

The three-dimensional image is very intuitive,informative,and vivid,and it is a very important carrier for facilitating information exchange.With the rapid development of multimedia technology,the high-efficiency,reliable transmission and security of three-dimensional images are increasingly attracting the attention of scholars.The joint compression and encryption of three-dimensional images is an important research content in the field of image encryption.Existing image joint compression and encryption algorithms are mainly based on compressive sensing and optical encryption techniques or chaotic system.Most of these image encryption methods are based on two-dimensional compressive sensing methods,and do not consider the use of tensor compression sensing techniques in image compression and encryption algorithm.Tensor compressive sensing technology is introduced in three-dimensional image encryption to realize the compression and encryption of image data,which is beneficial to the transmission and storage of images.It is of great significance to develop additional keys using the tensor model.Fractional random transformation is suitable for image encryption because of its good randomness.However,the existing two-dimensional discrete random transformation can not directly encrypt the three-dimensional image.Therefore,it is of great significance to construct a three-dimensional discrete fractional random transform to directly encrypt three-dimensional images.In order to enrich the image encryption algorithm based on compressive sensing,in this dissertation,two new algorithms are proposed by combining tensor compression sensing technique with three-dimensional discrete fractional random transformation and three-dimensional Lorenz chaos system to achieve joint compression and encryption of three-dimensional images.The main work and research results of this thesis are as follows:?1?A joint image compression and encryption algorithm is proposed based on three dimensional smooth l₀ norm?3D-SL0?and three-dimensional discrete fractional random transformation?3D-DFrRT?.The tensor compressive sensing technology is used to compress three-dimensional images,then the chaotic map is used to construct the fractional random transform kernel,and the three-dimensional fractional random transform is constructed by the tensor technique to realize the re-encryption of the ciphertext tensor.In the decoding stage,the discrete fractional random transformation with inverse fractional order is performed first,and then,based on the two-dimensional smooth₀l norm,the three-dimensional smooth₀l norm algorithm is extended by the tensor method,so as to realize the accurate reconstruction of the ciphertext image.The reconstructed image is obtained by setting different compression ratios,and the peak signal-to-noise ratios corresponding to different compression ratios are analyzed to show its compression reconstruction performance.Then the parameter keys are analyzed to analyze the safety performance.?2?A three-dimensional image joint compression and encryption algorithm is proposed based on orthogonal optimization tensor compression sensing?OTCS?and three-dimensional Lorenz chaotic system.A suitable tensor compression sensing method is designed to decompose the three-dimensional image tensor into a core tensor and three perceptual matrices.The gradient descent method is used to find the optimal solution to optimize the initial measurement matrix.Then the measurement matrix is embedded into the dynamic equations of the three-dimensional Lorenz chaotic system.The hyper-chaotic sequence is used to encrypt the optimal measurement matrix to achieve synchronization between encoding and decoding.Using the tensor different from the matrix processing,that is,the tensor expansion mode,excavate an additional key.Finally,reconstruction performance comparison analysis and security analysis are performed.The simulation results show that the proposed joint image compression encryption algorithm has the advantages of good compression and reconstruction performance,high key sensitivity,large key space,and strong anti-attack ability.It can achieve high compression of image data while ensuring the security of the image.