Hyperparameter selection for OSEM SPECT reconstruction in mesh domain with total variation regularization

Abstract

The purpose of this study was investigation of the <i>L</i>-curve method performance for the optimized hyperparameter selection in <i>maximum a posteriori</i> (MAP) Ordered Subsets Expectation Maximization (OSEM) Single Photon Computed Emission Tomography (SPECT) reconstruction in mesh domain with Total Variation (TV) regularization for different noise levels and three different mesh resolutions. Reconstruction with TV prior requires tuning of only one Bayesian hyperparameter &beta;. This was accomplished by application of the <i>L</i>-curve method. We analyzed the reconstructed image quality for various values of &beta; and investigated the relationship between the optimized &beta;, the mesh structure and the noise level in the projection data. We have found that each obtained L-curve exhibited one well-defined minimum and the optimal trade-off between noise and spatial resolution in the reconstructed images occurred for the value of &beta; defined by that minimum. The <i>L</i>-curves minima shifted towards lower values with increasing mesh resolution and towards higher values with increasing noise in the SPECT data. The shape of the <i>L</i>-curve depended on the mesh resolution and the noise level. By analyzing the reconstructed image quality, we have verified that the <i>L</i>-curve method is a suitable tool for estimation of the optimized value for the hyperparameter.