A locally adaptive regularization of a hybrid variational model for color image diffusion via integration of diffusion with normalized data

This paper presents a control of adaptive regularization for a hybrid variational model and its application to the denoising of color images, which combines total variation (TV) and [Formula: see text] regularizers with normalized data fidelity. The designed adaptive control works locally and is performed by a control parameter that intelligently selects the appropriate diffusion operator for smoothing (quadratic) and edge preservation (nonquadratic). In addition to combined diffusion operators, data term was normalized to ensure good balance between diffusion and fidelity terms. The idea of complementary data normalization enhances performance under high noise levels and mitigates artifacts. The resulting optimization framework leads to a time-dependent partial differential equation that is discretized using standard finite differences. Simulation experiments on benchmark data sets demonstrated that the proposed method consistently outperformed over conventional denoising techniques in terms of edge preservation, noise reduction and computational efficiency. Quantitative evaluation was performed using the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), root mean square error (RMSE), and convergence time (CT). A comparative analysis with state-of-the-art variational denoising models further highlights good performance of proposed approach in preserving sharp structural details while achieving effective noise suppression.