JSM 2005 Online Program

Abstract #302395

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	468
Type:	Invited
Date/Time:	Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
Sponsor:	Section on Statistical Computing
Abstract - #302395
Title:	Spatially Adaptive Smoothing: A Propagation-Separation Approach for Imaging Problems
Author(s):	Joerg Polzehl*+ and Vladimir Spokoiny
Companies:	WIAS and WIAS
Address:	Mohrenstr. 39, Berlin, International, D-10117, Germany
Keywords:	imaging ; nonparametric ; adaptive ; smoothing ; regression ; denoising
Abstract:	Adaptive weights smoothing (AWS) was introduced in Polzehl and Spokoiny (2000) in the context of image denoising. The procedure has some remarkable properties such as preservation of edges and contrast, and (in some sense) optimal reduction of noise. The procedure is fully adaptive and dimension-free. Simulations with artificial images show AWS is superior to classical smoothing techniques, especially when the underlying image function is discontinuous and can be well approximated by a piecewise constant function. However, the latter assumption can be rather restrictive for a number of potential applications. We have now revised and extended our approach to more general settings, including likelihood-based models (e.g., binary or Poisson regression) and the case of an arbitrary local linear parametric structure. In this talk, we establish some important results about properties of the new ''propagation-separation'' procedure, including rate optimality in the pointwise and global sense. The performance of the procedure is illustrated by examples of local constant and local polynomial reconstructions of images.

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