Improvements in quality and quantification of 3D PET images

The spatial resolution of Positron Emission Tomography is conditioned by several physical factors, which can be taken into account by using a global Point Spread Function (PSF). In this thesis a spatially variant (radially asymmetric) PSF implementation in the image space of a 3D Ordered Subsets Expectation Maximization (OSEM) algorithm is proposed. Two different scanners were considered, without and with Time Of Flight (TOF) capability. The PSF was derived by fitting some experimentally acquired images of a Na22 cylindrical source reconstructed with an OSEM algorithm. The fitting function took into account the post-filter applied on the images, the actual position of the point source, the source dimensions and the intrinsic discretization along the axial direction due to the finite dimensions of the slices. The proposed method of measurement was also validated and demonstrated its good accuracy in building the PSF model, justifying its use. The implementation of the PSF consisted in a redefinition of the projector and backprojector of the 3D OSEM algorithm. The continuous model of the PSF has been discretized by calculating its integral for each voxel in the image, allowing for a better adaptive implementation for each specific reconstruction FOV and pixel size. The explicit expression for the transposed PSF operator was also derived, showing that - in the spatially variant case - this does not coincide with the transpose of the PSF kernel. The PSF was tested on some phantom and clinical data: the results showed improved quantitative accuracy, spatial resolution and image quality; furthermore, the combined use of TOF and PSF appeared to allow them to take advantage of each other, leading to the best results. Unfortunately, a common effect of iterative reconstruction techniques is the increase of noise as iterations proceed, due to the ill-posed nature of the reconstruction problem. This is in contrast with the requirements of a PSF-aware algorithm, since the speed of convergence is lower than in non-PSF algorithms and, therefore, more iterations would be required to reach a sufficient convergence. Another important effect observed in PSF-based reconstructions is the enhancement of regions with sharp intensity transitions. In this thesis it was demonstrated to be strongly related to the implementation of the spatial resolution recovery and, even in presence of a perfectly matched kernel, unavoidable unless an unpractical number of iterations is used. Regularization techniques have been demonstrated to be useful for taking noise under control during the reconstruction and improving the benefits from the use of the PSF information by increasing the number of iterations used. In particular, in this thesis a Bayesian variational regularization strategy has been tested and employed. Two good candidates for the use in PET practice are the Huber (or Gauss-Total Variation) and the generalized p-Gaussian priors. In this thesis a modification of the p-Gaussian prior was proposed to maintain the smoothing effect for low gradients (i.e. in background regions) and to reduce the spatial resolution loss, while retaining "natural" transitions and appearance in the image. The considered priors depend on some regularization parameters. In this thesis a figure of merit, taking into account both the qualitative and the quantitative content, was proposed to evaluate the global "detectability" of a lesion. The validation of this detectability index showed a very good correlation with the human response and, thus, justified its use to set the regularization parameters. The regularization parameters were then determined by maximizing the detectability index for each prior. This optimization was performed for a sphere with diameter 10 mm and 10 OSEM iterations. The validation of the proposed modifications was quantitative on data acquired with a NEMA IEC Body Phantom and qualitative on data relative to two oncological patients and consisted of a comparison between the standard reconstruction algorithms, the proposed algorithm, the results obtained with the p-Gaussian prior and with Gauss-Total Variation. This comparison showed an effective control of noise (but with natural appearance of the image) by the proposed prior with a contemporary good preservation of spatial resolution, contrast and definition of the activity distribution. Moreover, the proposed prior was shown to be able also to take the edge artefact under control, drastically reducing the overshoots originating at large transitions in the image. Positive results were obtained also when the regularization strategy was used in conjunction with the TOF information, suggesting a possible future employment in the PET reconstruction framework.