The Image Encryption Method Based on Deep Learning and Compressed Sensing

Image encryption utilizes the two-dimensional matrix characteristics of digital images to convert recognizable, information-rich images into indistinguishable, noise-like images by applying reversible transformation rules in the spatial domain. Traditional image encryption techniques include chaotic encryption, optical encryption, spatial domain encryption, and DNA encryption. However, some traditional methods face limitations in decryption quality and security, making them susceptible to brute-force attacks or statistical analysis. To address these issues, this paper proposes an image encryption method based on deep learning and compressed sensing. The main innovations lie in three aspects. Firstly, chaotic sequences generated by iterating the initial values of a six-dimensional cellular neural network system are used as a dataset, which is then divided into training and testing sets and input into a convolutional neural network for processing. Secondly, two measurement matrices are used for two-dimensional compressed sensing of the image, one derived from the Logistic chaotic system and the other being a random measurement matrix. Thirdly, during the encryption process, the processed prediction results from the test set are used to scramble the image. The scrambled image is then converted into a matrix and XORed with a newly processed measurement matrix generated by the Logistic chaotic system to produce a new matrix. This new matrix is then used to XOR encrypt the image, generating the encrypted output.

I. Introduction

Image data, known for its vast informational content and significant redundancy, has become an invaluable resource in the modern digital world. However, this richness also brings challenges-transmitting large volumes of image data over networks typically requires substantial bandwidth, imposing significant pressure on transmission efficiency and costs. The theory of compressed sensing, proposed by Candes, Donoho, Romberg, and Tao ^[1]–[2], leverages the sparsity of signals in specific transform domains, enabling compression and efficient reconstruction of signals at rates far below the Nyquist sampling rate, thus drastically reducing the volume of data needed for transmission. To address these challenges, reference [3] proposed a universal image encryption algorithm applicable to both grayscale and RGB color images. This algorithm combines bilinear interpolation and convolutional neural networks for image compression, followed by a hybrid chaotic system composed of a two-dimensional cloud model and Logistic mapping to encrypt and decrypt the compressed image through sliding scrambling and vector decomposition, ultimately reconstructing the decrypted image. This paper presents a novel image compression and encryption algorithm that achieves significant improvements in both compression and encryption performance.