Validation of training set approaches to hyperparameter estimation for Bayesian tomography

Soo-Jin Lee

doi:10.1117/12.739440

24 September 2007 Validation of training set approaches to hyperparameter estimation for Bayesian tomography

Soo-Jin Lee

Author Affiliations +

Proceedings Volume 6696, Applications of Digital Image Processing XXX; 66962F (2007) https://doi.org/10.1117/12.739440
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

Since algorithms based on Bayesian approaches contain hyperparameters associated with the mathematical model for the prior probability, the performance of algorithms usually depends crucially on the values of these parameters. In this work we consider an approach to hyperparameter estimation for Bayesian methods used in the medical imaging application of emission computed tomography (ECT). We address spline models as Gibbs smoothing priors for our own application to ECT reconstruction. The problem of hyperparameter (or smoothing parameter in our case) estimation can be stated as follows: Given a likelihood and prior model, and given a realization of noisy projection data from a patient, compute some optimal estimate of the smoothing parameter. Among the variety of approaches used to attack this problem in ECT, we base our maximum-likelihood (ML) estimates of smoothing parameters on observed training data, and argue the motivation for this approach. To validate our ML approach, we first perform closed-loop numerical experiments using the images created by Gibbs sampling from the given prior probability with the smoothing parameter known. We then evaluate performance of our method using mathematical phantoms and show that the optimal estimates yield good reconstructions. Our initial results indicate that the hyperparameters obtained from training data perform well with regard to percentage error metric.

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Soo-Jin Lee "Validation of training set approaches to hyperparameter estimation for Bayesian tomography", Proc. SPIE 6696, Applications of Digital Image Processing XXX, 66962F (24 September 2007); https://doi.org/10.1117/12.739440

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KEYWORDS

Data modeling

Brain

Tomography

Sensors

Mathematical modeling

Reconstruction algorithms

Gamma radiation

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