Optical EngineeringTraining set approach to smoothing parameter estimation for spline-regularized tomographic reconstruction
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Since algorithms based on Bayesian approaches contain smoothing parameters associated with the mathematical model for the prior probability, the performance of algorithms usually depends crucially on the values of these parameters. We consider an approach to smoothing parameter 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 smoothing parameter estimation can be stated as follows. Given a likelihood and prior model, and given a realization of noisy projection data, compute some optimal estimate of the smoothing parameter. We focus on the estimation of the smoothing parameter for mathematical phantom studies. Among the variety of approaches used to attack this problem, we base our maximum-likelihood (ML) estimates of smoothing parameters on observed training data. 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 the performance of our method using mathematical phantoms and show that the optimal estimates obtained from training data yield good reconstructions in terms of a percentage error metric.