Deep Learning-Based Image Watermarking Using Catalan Transform and Non-Negative Matrix Factorization

In the digital age, embedding imperceptible data into images for authenticating ownership and content integrity through watermarking has gained immense importance. Existing watermarking methods struggle to balance imperceptibility, robustness, and security, resulting in suboptimal peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), normalized correlation (NC) values, along with higher time complexity. To overcome these constraints, this study proposes a new method for image watermarking that uses deep learning and operates within the YIQ color space. The main contribution of the proposed method is its new combination of the Catalan transform (CT) and non-negative matrix factorization (NMF) with an artificial neural network (ANN) for enhanced watermark embedding and extraction. CT enhances pixel intensity while NMF extracts the most significant features from each (m x m) block (with m= 2 in simulations), improving the method’s robustness and imperceptibility. Before embedding, the watermark undergoes a new scrambling technique combining adaptive diffusion and non-linear transform, significantly enhancing security. A new embedding equation integrates the watermark into the non-negative elements of the host image blocks. Statistical features from watermarked blocks are used to create a dataset for extraction, and an ANN model trained on this dataset enables accurate watermark recovery. The proposed method achieves a PSNR of 66.43 to 77.02 dB (31.91% improvement), SSIM of 0.99 to 1.00 (1.02% improvement), and NC of 0.99 to 1.00 (1.88% improvement). Its computational complexity is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>), a 33.33% reduction compared to traditional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>) methods. Security metrics include RE = 0.3094, UACI = 34.21%, and NPCR = 99.15%, demonstrating superior robustness and efficiency over existing approaches.