Evaluation of the utility of estimated covariance kernels for predicting regional ensemble variance

PET reconstruction results in images with correlations between neighbouring image voxels. Alternative reconstruction algorithms, such as OSEM reconstruction incorporating resolution modelling (RM) can significantly alter this voxel covariance. While RM has been demonstrated to reduce voxel variance, it has been suggested that the increased covariance results in increased region-based ensemble variance (EV). The aim of this work was to develop and evaluate methods to estimate covariance kernels and evaluate their utility in predicting ensemble variance (EV). The end goal of the work is to enable tools for comparing regional EV from reconstruction algorithms with very different correlation structures and in a way that can be derived from routine clinical PET data. Fifty sequential 2.5 minute images of a uniform Ge-68 phantom were acquired on a Siemens Biograph mCT. Images were reconstructed: with and without RM (Siemens HD-PET); and with isotropic voxel dimensions of 2 mm and 4 mm. A 40 mm × 40 mm × 40 mm cube of voxels were extracted from the centre of image and used to estimate covariance kernels. Spherical regions of different diameters (40 mm max) drawn on the uniform phantom were used to estimate EV of the mean regional concentration using the 50 image replicates. This was compared against estimates of EV derived from the covariance kernels. Estimation involved convolving a mask of unit volume defining the region shape, with the covariance kernel before sampling the mean value of the resulting image within the region. As expected estimated covariance kernels when RM was used were broader. Good agreement (-40% to +30%) was observed between the measured EV and values estimated from the covariance kernels. RM and larger image voxels showed reduced EV values for small spherical regions. For large regions only very small differences in EV were observed between reconstruction algorithms. The use of Fourier methods to derive voxel covariance kernels appears to show promise.