An estimator for functional data with application to MRI.

Abstract:

:We propose a method for restoring the underlying true signal in noisy functional images. The Nadaraya-Watson (NW) estimator described in, e.g., [1] is a classical nonparametric estimator for this problem. Since the true scene in many applications contains abrupt changes between pixels of different types, a modification of the NW estimator is needed. In the data we study, the characteristics of each pixel are given as a function of time. This means that a curve of data points is observed at each pixel. Utilizing this time information, the NW weights can be modified to obtain a weighted average over pixels with the same true value. Theoretical results showing the estimator's properties are developed. Several parameters play an important role for the restoration result. Practical guidelines are given for how these parameters can be selected. Finally, we demonstrate how the method can be successfully applied both to artificial data and Magnetic Resonance Images.

journal_name

IEEE Trans Med Imaging

authors

Godtliebsen F,Chu CK,Sørbye SH,Torheim G

doi

10.1109/42.906423

subject

Has Abstract

pub_date

2001-01-01 00:00:00

pages

36-44

issue

1

eissn

0278-0062

issn

1558-254X

journal_volume

20

pub_type

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