an adaptive perona{malik model with coupled gradient weight and gradient-dependent fidelity

We propose an image denoising model based on partial differential equations that extends the classical perona{malik anisotropic diffusion method. the diffusion coefficient depends on the image gradient and controls smoothing, while a gradientdependent fidelity term adjusts adherence to the noisy image. this approach reduces noise in flat regions and preserves edges and fine details. experiments on standard test images show improvements in peak signal-to-noise ratio and structural similarity index, demonstrating effective edge-preserving denoising.