Denoising of MR images using Kolmogorov-Smirnov distance in a Non Local framework

Data coming from any acquisition system, such as Magnetic Resonance Imaging ones, are affected by noise. Although modern high field scanners can reach high Signal to Noise Ratios, in some circumstances, for example in case of very weak signals due to a specific acquisition sequence, noise becomes a critical issue that has to be properly handled. In the last years methods based on the so called Non Local Mean have proven to be very effective in denoising tasks. The idea of these filters is to find similar patches across the image and to jointly exploit them to obtain the restored image. A critical point is the distance metric adopted for measuring similarity. Within this manuscript, we propose a filtering technique based on the Kolmogorov-Smirnov distance. The main innovative aspect of the proposed method consists of the criteria adopted for finding similar pixels across the image: it is based on the statistics of the points rather than the widely adopted weighted Euclidean distance. More in details, the Cumulative Distribution Functions of different pixels are evaluated and compared in order to measure their similarities, exploiting a stack of images of the same slice acquired with different acquisition parameters. To quantitatively and qualitatively assess the performances of the approach, a comparison with other widely adopted denoising filters in case of both simulated and real datasets has been carried out. The obtained results confirm the validity of the proposed solution.