Abstract: In various applications, including magnetic resonance imaging (MRI) and functional MRI (fMRI), 3-D 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.

Brief Biography of the Speaker:
Peihua Qiu got his Ph.D. in statistics from the Statistics Department at the University of Wisconsin at Madison in 1996. He worked as a senior research consulting statistician of the Biostatistics Center at the Ohio State University during 1996-1998. Then, he worked as an assistant professor (1998-2002), an associate professor (2002-2007), and a full professor (2007-present) of the School of Statistics at the University of Minnesota. He is an elected fellow of the American Statistical Association, an elected fellow of the Institute of Mathematical Statistics, an elected member of the International Statistical Institute, and a lifetime member of the International Chinese Statistical Association. His major research interests include nonparametric regression, jump curve and surface estimation, image processing, quality control, reliability and survival analysis, and various statistical applications. So far, he has published over 50 research papers in refereed journals. His research monograph titled Image Processing and Jump Regression Analysis (2005, Wiley) won the inaugural Ziegel prize in 2007, for its contribution in bridging the gap between jump regression analysis in statistics and image processing in computer sciences. He is the current associate editor of the Journal of the American Statistical Association and Technometrics, and the guest co-editor of Multimedia Tools and Applications. In 2010, he is the plenary speaker of the annual meeting of the German Statistical Society, and the featured speaker with discussions of the Technometrics invited session during the Joint Summer Meeting of the American Statistical Association.