Locally Enhanced Denoising Method for MRI Imaging using the Schrodinger Operator

Abstract

In this paper, an adaptive method for Magnetic Resonance (MR) image denoising is proposed, based on the Semi-Classical Signal Analysis (SCSA). The SCSA employs the squared eigenfunctions of the Schrodinger operator, whose potential is considered to be the noisy image. However, the low performance of the method, using single-valued parameters $h$ and $\gamma$, is mainly due to the non-uniform distribution of the noise in the MR image. This non-uniformity is related to multiple factors such as the used modality, electrical noise, and other artifacts related to the patient. To overcome this challenge, the proposed adaptive SCSA algorithm locally optimizes the pair (h,gamma), using a grid segmentation, to introduce an appropriate distribution along the different sub-images of the grid. This adaptation to the spatial variation of noise responds efficiently to the denoising objectives. Numerical tests using synthetic datasets from BrainWeb and real MR images show the effectiveness of the proposed method. The obtained results are also compared to the conventional case.