The ability of a denoising procedure to preserve fine image structures when suppressing unwanted noise has crucial importance for an accurate and effective medical diagnosis. We introduce here a new procedure of edge-preserving denoising for medical images, that combines the flexibility in prior assumptions, and computational effectiveness of parametric multi-quadratic dynamic programming with the increased accuracy of a tree-like representation of a discrete lattice based on the full set of possible adjacency graphs of image elements. Proposed procedure can effectively remove an additive white Gaussian noise with high quality. We provide experimental results in image denoising as well as comparison with related methods.