A Greedy Algorithm-Based Scheme for High-Quality Visually Meaningful Image Encryption

Abstract To address the limitations of existing visually meaningful image encryption algorithms in terms of visual quality 
and adaptability across different wavelet types, this paper introduces a novel greedy algorithm-based embedding method. 
Our approach innovatively selects the optimal decomposition basis dynamically by calculating an error value for each 
candidate basis, tailored to the specific characteristics of both the host and plaintext images. This error-based 
selection process significantly enhances visual quality across a spectrum of wavelet transformations. Furthermore, 
we propose a novel two-dimensional hyperchaotic map (2D-RECM), characterized by its hyperchaotic behavior across a 
broad range of control parameters. The integration of 2D-RECM with our embedding algorithm results in a robust visually 
meaningful image encryption algorithm (RECM-VMIEA). Extensive simulations and analyses confirm that RECM-VMIEA not only 
maintains high visual quality but also exhibits exceptional security and robustness, outperforming existing algorithms 
in these critical aspects.