Automated MRI restoration via recursive diffusion

Denoising is an integral step in the automated analysis of Magnetic Resonance (MR) images. A computationally fast restoration algorithm with a minimum number of operational parameters and appreciably good edge-preserving characteristics is missing in the literature. To fill these gaps, an edge-preserving filter based on the principles of iterative diffusion and Beltrami flow is introduced in this paper. The value of the restored intensity at an arbitrary location during current iteration is a sum of two distinct terms. First term is the cumulative sum of flow values corresponding to its 8-connected neighbours, scaled by an arbitrary normalization constant. The second term is the restored intensity corresponding to that pixel computed in the previous iteration. The optimum value of the number iterations in the algorithm is determined with the help of a newly designed Target Function (TF). The TF is the absolute difference between Relative Statistics of Noise (RSN) and Relative Strength of Dominant Edges (RSDE). The proposed target function has shown good concordance with the subjective quality of output images at different values of the number of iterations. The proposed Optimized Beltrami Flow-based Iterative Diffusion filter (OBFID) is found to be superior to other filters in terms of the ability to preserve the edge strength and suppress noise. It is computationally fast compared to other filters.