Edge structure preserving 3D image denoising by local surface approximation

In various applications, including magnetic resonance imaging (MRI) and functional MRI (fMRI), 3D images are becoming increasingly popular. To improve the reliability of subsequent image analyses, 3D image denoising is often a necessary preprocessing step, which is the focus of the current paper. In the literature, most existing image denoising procedures are for 2D images. Their direct extensions to 3D cases generally cannot handle 3D images efficiently because the structure of a typical 3D image is substantially more complicated than that of a typical 2D image. For instance, edge locations are surfaces in 3D cases which would be much more challenging to handle compared to edge curves in 2D cases. We propose a novel 3D image denoising procedure in this paper, based on local approximation of the edge surfaces using a set of surface templates. An important property of this method is that it can preserve edges and major edge structures (e.g., intersections of two edge surfaces and pointed corners). Numerical studies show that it works well in various applications.