Research on Image Authentication Technology Based on Sparse Approximation and Quantum Encryption

This paper aims to explore and apply a novel image authentication technology that integrates Sparse Approximation (SA), Quantum Encryption (QE), and Measurement Matrix (MM) to address the issues of integrity verification, copyright protection, and tamper resistance in the transmission and storage of digital images. With the widespread adoption of digital technology, images are susceptible to unauthorized modifications, and traditional authentication techniques struggle to balance robustness, security, and processing efficiency. This paper designs a preprocessing process involving watermark quad-segmentation, transform domain DCT sparsification, and sparse coefficient exchange, employs quantum logic mapping (λ=3.9, δ=0.01) to generate the measurement matrix, and constructs a full-chain technology solution encompassing "preprocessing-encryption-dual watermark embedding-recovery-verification". Experiments are conducted based on standard test images from the USC-SIPI image database. By comparing metrics such as Peak Signal-to-Noise Ratio (PSNR), Normalized Cross-Correlation (NCC), Mean Structural Similarity Index (MSSIM), and Normalized Absolute Error (NAE), the experiments verify the superiority of this technology in resisting noise (Gaussian noise, salt-and-pepper noise), geometric attacks (rotation, scaling), and enhancement attacks (Gaussian low-pass filtering, median filtering): PSNR reaches 42.78dB and NCC is nearly 0.9999 in the absence of attacks, and NCC still maintains 0.9989 under Gaussian noise (0.01 variance). This technology provides a solution for digital image authentication that combines high security with high efficiency, and can be applied in forensic investigation, copyright protection, secure communication, and other fields. It has positive significance for the in-depth research and wide application of image authentication technology.