We present a novel anisotropic diffusion algorithm for noise reduction in Magnetic Resonance Imaging (MRI). The method integrates two key concepts: (1) diffusion is explicitly constrained to avoid increases in local image gradients, thereby preserving edges and fine structural details; and (2) a sequence of filters with exponentially increasing radii is applied, each maintaining a fixed number of non-zero coefficients. These filters allow the algorithm to evaluate whether pixels distant from the target location can contribute to smoothing without degrading local gradients. As a result, the method aims to balance between preserving local details and averaging global similarities. In contrast to traditional denoising techniques based on local filtering or total variation minimization, the proposed algorithm enables controlled non-local diffusion and naturally extends to three-dimensional voxel arrays, making it well-suited for volumetric MRI data. The framework also permits the integration of additional geometric constraints, such as curvature, further enhancing its ability to preserve anatomical structures and surfaces. The effectiveness of the proposed method is demonstrated on real MRI data from a macaque monkey. The experimental results indicate PSNR values comparable to those of our previous approach, while providing substantially better suppression of low-frequency noise, absence of visible artifacts, and faithful preservation of critical image features.