Computationally efficient hybrid multi-domain transform fusion for secure image steganography using rate–distortion optimization and Toom–Cook acceleration

In the era of extensive developmental growth, multimedia communication systems demand protective and indiscernible information-hiding techniques that can maintain a balance between robustness, capacity, and computational efficacy. The research gap analysis highlights the necessity for a mathematically defined steganographic strategy that integrates rate–distortion optimization, knowledge-based adaptive embedding, hybrid domain modeling, and statistical invisibility constraints in a non-heuristic approach toward scalable high-capacity transmission systems. The novelty of the proposed strategy lies in the combination of rate–distortion optimization, adaptive CNN-based control for embedding, and histogram preservation of frequency channel embedding within a consolidated information-hiding architecture, within illuminated components of color areas. This ensures observable fidelity and configurational stability. To generate an adaptive embedding-based probability map, a lightweight convolutional neural network that enables a content-aware embedding dependent on local picture complexity is incorporated. Moreover, incorporating a histogram-preservation restriction reduces sensitivity to classical and learning-guided steganalysis and increases analytical security. Furthermore, Toom–Cook accelerated convolution is utilized to achieve improved computational scalability through accelerated transform-domain convolution, ensuring scalability for high-resolution images. Experimental analysis illustrates excellent performance with superior imperceptibility in average values obtained for a peak signal-to-noise ratio (PSNR) maintained above 50 dB (≈51.40 dB) and average structural similarity index measure (SSIM) ≈0.9816, low bit error rates, and near-random detectability (area under curve ≈0.5). Comparative and ablation analyses confirm that the proposed framework outperforms existing spatial, transform-domain, and deep learning-based methods. The proposed approach provides a unified, theoretically constrained, and scalable solution for secure high-capacity image steganography.