A multi-resolution and adaptive 3-D image denoising framework with applications in medical imaging

Due to recent increase in the usage of 3-D magnetic resonance images (MRI) and analysis of functional magnetic resonance images, research on 3-D image processing becomes important. Observed 3-D images often contain noise which should be removed in such a way that important image features, e.g., edges, edge structures, and other image details should be preserved, so that subsequent image analyses are reliable. Most image denoising methods in the literature are for 2-D images. However, their direct generalizations to 3-D images cannot preserve complicated edge structures well. Because, the edge structures in a 3-D edge surface can be much more complicated than the edge structures in a 2-D edge curve. Moreover, the amount of smoothing should be determined locally, depending on local image features and local signal to noise ratio, which is much more challenging in 3-D images due to large number of voxels. This paper proposes an efficient 3-D image denoising procedure based on local clustering of the voxels. This method provides a framework for determining the size of bandwidth and the amount of smoothing locally by empirical procedures. Numerical studies and a real MRI denoising show that it works well in many medical image denoising problems.