Image Compression And Encryption Algorithm Based On Chaos Measurement Matrix And Compressive Sensing

With the rapid development of network technology,digital images are widely used in all walks of life;because the image can intuitively display the contained information,it is widely used in many fields,such as banking,military,medicine,finance and so on.Once these images containing important information are spread on the Internet,they are likely to be attacked and cracked by hackers,which will cause unpredictable consequences.Encrypting images make meaningful images meaningless,which can effectively protect the security of these private information in transmission and storage.Compressive sensing(CS)technology has been gradually used in image encryption in recent years.While compressing the image,it also implements data encryption to obtain ciphertext images,which not only protects the security of the information,but also saves more transmission bandwidth,transmission time and storage space.Signal sparsity,measurement matrix generation and reconstruction algorithm are the core content of compressive sensing theory,in which the quality of measurement matrix will directly affect whether the signal is easily sampled by hardware and whether the signal can be correctly reconstructed.In the image compression and encryption algorithm based on CS,the current measurement matrix is mostly generated by chaotic system,but the randomness is not strong,resulting in the performance of the measurement matrix is not very good,which has a certain impact on the quality of the reconstructed image.In addition,the scrambling and diffusion methods of some algorithms are not very random,which reduces the security of the algorithms.In order to solve these problems,combined with chaos system,compressive sensing,scrambling-diffusion and other technologies,carried out the research of measurement matrix construction and image compression-encryption algorithms,and the main research contents are as follows:(1)A measurement matrix optimization algorithm based on adaptive step size gradient descent is designed.Based on this,an image compression and encryption algorithm based on compressive sensing and double random phase coding is proposed.In the optimization algorithm,first the eigenvalue decomposition of the Gram matrix is used,then shrink the non-diagonal elements in the Gram matrix,and then use gradient descent to approach the ETF;the Barzilai-Borwei method and the Armijo criterion are combined to make the step size adaptively adjusted,and then the output measurement matrix is optimized by QR decomposition,and finally the optimized measurement matrix is obtained.At the same time,in the image compression and encryption algorithm,the plaintext image is first discrete wavelet decomposed to obtain an approximate component and three detail components,then the index vector is used to scramble the approximate component and the three detail components,and then use two different measurement matrices to compress and measure the detail components separately,and then use the scrambled approximation components as the real part,and combine the three measurement value matrices as the imaginary parts to form a new matrix.Next,this new matrix is encoded with double random phases,and the real and imaginary parts of the transformed matrix are quantized and diffused separately,and finally a ciphertext image is obtained.The experimental results show the feasibility of the proposed measurement matrix optimization algorithm and the corresponding image compression and encryption algorithm.(2)A color image compression encryption algorithm based on compression sensing and double random encryption mechanism is proposed.Firstly,the color plaintext image is decomposed into three components of R,G,and B,and then DWT is applied to them,then perform double random position scrambling on the sparse coefficient matrices.Secondly,the scrambled matrix is compressed and quantized separately,and then double random pixel value diffusion is carried out between and inside the R,G and B components at the same time,and finally a color ciphertext image is obtained.The experimental results show the feasibility of the encryption algorithm.(3)A color image compression encryption algorithm based on 4D memristive chaotic system and two-dimensional compressed sensing is proposed.First,the color plaintext image is decomposed into three components,R,G,and B,and then its two-dimensional discrete wavelet transform is used to obtain a sparse coefficient matrix.Secondly,the sparse coefficient matrix is subjected to two-dimensional compressive sensing and quantization,and then Arnold map and indexing are used.The vector performs double random position scrambling on the quantized matrix,and the quantized matrix is diffused by multiple random pixel values at the same time within R,G,and B components.Finally,the ciphertext image is obtained.The experimental results show the effectiveness of the encryption algorithm.