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Penalized likelihood (PL) reconstruction has demonstrated potential to improve image quality of positron emission tomography (PET) over unregularized ordered-subsets expectation-maximization (OSEM) algorithm. However, selecting proper regularization parameters in PL reconstruction has been challenging due to the lack of ground truth and variation of penalty functions. Here we present a method to choose regularization parameters using a cross-validation log-likelihood (CVLL) function. This new method does not require any knowledge of the true image and is directly applicable to list-mode PET data. We performed statistical analysis of the mean and variance of the CVLL. The results show that the CVLL provides an unbiased estimate of the log-likelihood function calculated using the noise free data. The predicted variance can be used to verify the statistical significance of the difference between CVLL values. The proposed method was validated using simulation studies and also applied to real patient data. The reconstructed images using optimum parameters selected by the proposed method show good image quality visually.

A single photon emission computed tomography (SPECT) rotating slat collimator with strip detector acquires distance-weighted plane integral data, along with the attenuation factor and distance-dependent detector response. In order to image a 3D object, the slat collimator device has first to spin around its axis and then rotate around the object to produce 3D projection measurements. Compared to the slice-by-slice 2D reconstruction for the parallel-hole collimator and line integral data, a more complex 3D reconstruction is needed for the slat collimator and plane integral data. In this paper, we propose a 3D RBI-EM reconstruction algorithm with spherically-symmetric basis function, also called 'blobs', for the slat collimator. It has a closed and spherically symmetric analytical expression for the 3D Radon transform, which makes it easier to compute the plane integral than the voxel. It is completely localized in the spatial domain and nearly band-limited in the frequency domain. Its size and shape can be controlled by several parameters to have desired reconstructed image quality. A mathematical lesion phantom study has demonstrated that the blob reconstruction can achieve better contrast-noise trade-offs than the voxel reconstruction without greatly degrading the image resolution. A real lesion phantom study further confirmed this and showed that a slat collimator with CZT detector has better image quality than the conventional parallel-hole collimator with NaI detector. The improvement might be due to both the slat collimation and the better energy resolution of the CZT detector.