MME-Based Piecewise Data Transformation and 2D Mapping Optimization for Reversible Data Hiding

In reversible data hiding (RDH) based on prediction-error-expansion (PEE), the embedding distortion is lower for bit “0” than for bit “1”. To favor bit “0”, a binary matrix embedding (BME)-based data transformation strategy is introduced. In this strategy, the transformed data replaces the original, and embedding is performed via two-dimensional (2D) mappings. However, the mappings are restricted to at most two modification directions by BME, limiting flexibility and increasing distortion. Moreover, the embedded data distribution is altered by data transformation, rendering traditional mapping selection models inapplicable. To address the above problems, a multivariate matrix embedding (MME)-based 2D PEE framework is proposed in this paper. First, a piecewise data transformation strategy is introduced to enable embedding via generalized mappings with three modification directions. Then, the corresponding capacity-distortion model is established to optimize mapping selection. Finally, adaptive costs are refined based on mapping patterns to minimize the embedding distortion. Experimental results demonstrate that the proposed method achieves superior marked image quality over some state-of-the-art methods.