Kernel regression based feature extraction for 3D MR image denoising

Kernel regression is a non-parametric estimation technique which has been successfully applied to image denoising and enhancement in recent times. Magnetic resonance 3D image denoising has two features that distinguish it from other typical image denoising applications, namely the tridimensional structure of the images and the nature of the noise, which is Rician rather than Gaussian or impulsive. Here we propose a principled way to adapt the general kernel regression framework to this particular problem. Our noise removal system is rooted on a zeroth order 3D kernel regression, which computes a weighted average of the pixels over a regression window. We propose to obtain the weights from the similarities among small sized feature vectors associated to each pixel. In turn, these features come from a second order 3D kernel regression estimation of the original image values and gradient vectors. By considering directional information in the weight computation, this approach substantially enhances the performance of the filter. Moreover, Rician noise level is automatically estimated without any need of human intervention, i.e. our method is fully automated. Experimental results over synthetic and real images demonstrate that our proposal achieves good performance with respect to the other MRI denoising filters being compared.