Exploiting 2D-SDMCHM and matching embedding driven by flag-shaped hexagon prediction for visually meaningful medical image cryptosystem

With the proliferation of advanced medical technologies and smart wearable devices, a considerable volume of patient data and medical images is being generated and stored, leading to an escalating concern over patient privacy violations and manipulation. Therefore, safeguarding the secrecy and integrity of medical images is paramount for preserving patient privacy and ensuring accurate medical diagnostics. To tackle this challenge, this paper introduces a novel approach, the Visually Meaningful Medical Image Cryptosystem (VMMIC), leveraging a 2-Dimensional Sinusoidal Discrete Memristor Coupled Hyperchaotic Map (2D-SDMCHM) to protect the privacy of medical images. The innovation of this study is primarily reflected in three aspects: Firstly, a novel Discrete Memristor (DM) model is proposed, upon which a new 2D-SDMCHM is constructed. Comparative analysis showcases its superior chaos robustness, as evidenced by evaluations through bifurcation diagrams, phase trajectories, Lyapunov exponents, and Shannon entropy. Secondly, we introduce a measurement matrix optimization algorithm based on Optimal Matrix Arrangement (OMA) for Compressive Sensing (CS), aimed at minimizing the coherence of the measurement matrix, thereby enhancing reconstruction accuracy. Lastly, a Matching Embedding Method Driven by Flag-Shaped Hexagon Prediction (MEMFHP) is introduced to ensure lossless concealment of confidential information. Experimental findings and comparative evaluations affirm the VMMIC's capability to meet high standards of reconstruction quality, steganography, and efficiency in handling medical images, while also demonstrating robustness against various attacks. Consequently, the proposed VMMIC holds significant promise for practical implementation in engineering applications.