Invariant moments and transform-based unbiased nonlocal means for denoising of MR images

Nonlocal means (NLM) has been applied successfully to medical images degraded with signal independent additive Gaussian noise. However, magnetic resonance images (MRI) are generally corrupted with signal dependent Rician noise which follows Gaussian distribution at high signal-to-noise ratio (SNR) and Rayleigh distribution at low SNR. Considering these properties of the Rician noise, NLM is applied on the squared magnitude images after subtracting the bias term induced during the formation of MR data. In this paper, we propose the use of Zernike moments (ZMs)-based unbiased NLM approach for MRI denoising. ZMs belong to a family of orthogonal rotation invariant moments and possess many useful characteristics such as rotation invariance, minimum information redundancy and better noise resilience. The ability of ZMs to represent edges and fine structures in any orientation and provide better similarity measures make them more suitable for NLM based MRI denoising while preserving the significant details during the restoration process. In addition, we have also investigated the use of non-orthogonal rotation invariant Hu moments and angular radial transform (ART) for MRI denoising. Detailed experiments are conducted using standard clinical data sets to compare the performance of the proposed approaches with the existing approaches.