Edge Structure Preserving 3-D Image Denoising

In various applications, including magnetic resonance imaging (MRI) and functional MRI (fMRI), 3D images get increasingly popular. To improve reliability of subsequent image analyses, 3-D image denoising is often a necessary pre-processing step, which is the focus of the current paper. In the literature, most existing image denoising procedures are for 2-D images. Their direct extensions to 3-D cases generally can not handle 3-D images efficiently, because the structure of a typical 3-D image is substantially more complicated than that of a typical 2-D image. For instance, edge locations are surfaces in 3-D cases, which would be much more challenging to handle, compared to edge curves in 2-D cases. In this paper, we propose a novel 3-D image denoising procedure, by approximating the edge surfaces properly, using local smoothing and nonparametric regression methods. One important feature of this method is its ability to 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. Key–Words: Edge-preserving image restoration, jump regression analysis, surface estimation.