Poisson intensity estimation for tomographic data using a wavelet shrinkage approach

Author

Cavalier, Laurent ; Koo, Ja-Yong

Author_Institution

Centre de Mathematiques et Informatique, Univ. Aix-Marseille, Marseille, France

Volume

48

Issue

10

fYear

2002

fDate

10/1/2002 12:00:00 AM

Firstpage

2794

Lastpage

2802

Abstract

We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette decomposition (WVD), we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on Besov function classes. Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term.

Keywords

adaptive estimation; convergence of numerical methods; minimax techniques; nonlinear estimation; positron emission tomography; stochastic processes; wavelet transforms; 2D problem; Besov function classes; PET; Poisson intensity estimation; Poisson processes; adaptive estimator; emission density; empirical vaguelette coefficients thresholding; intensity function estimation; linear estimators; minimax convergence rate; nonlinear estimation; optimal convergence rate; positron-emission tomography; random mechanism; tomographic data; two-dimensional problem; wavelet shrinkage; wavelet-vaguelette decomposition; Computed tomography; Convergence; Inverse problems; Least squares methods; Maximum likelihood detection; Maximum likelihood estimation; Minimax techniques; Positron emission tomography; Statistics; Two dimensional displays;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2002.802632

Filename

1035132