Poisson intensity estimation for tomographic data using a wavelet shrinkage approach

• Published in: IEEE transactions on information theory Vol. 48; no. 10; pp. 2794 - 2802
• Main Authors: Cavalier, L., Ja-Yong Koo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2002; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive estimation; Adaptive systems; Convergence; Convergence of numerical methods; Data reduction; Density; Emission; Estimating techniques; Estimators; Inverse problems; Linear programming; Mathematical models; Minimax methods; Minimax technique; Nonlinear programming; Optimal systems; Optimization; Poisson distribution; Positron emission tomography; Random processes; Stochastic processes; Tomography; Wavelet transforms
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2002.802632

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.