Real-time PET image reconstruction based on regularized pseudo-inverse of the system matrix

The feasibility of tomographic image reconstruction by projection data filtering based on the singular value decomposition of the system matrix has recently been demonstrated in high-resolution animal positron emission tomography (PET). A regularization methodology involving truncation of the singular value spectrum based on the systematic spatial resolution analysis has been proposed and successfully applied. In the present paper, we show how real-time image reconstruction can be achieved using the regularized pseudo-inverse of the system matrix. An update of the current image estimate can be obtained using one column of the regularized pseudo-inverse matrix to account for the next registered event, thus allowing, in principle, for instant visualization of the radioactivity distribution while the object is still being scanned. Computed estimates converge to the minimum-norm least-squares solution of the regularized inverse problem when sufficient total counts are acquired to fulfill the assumption of the normal data error distribution. The computing expenses for image updating to account for the next registered event depend only on the total number of pixels in the discrete image representation. Data storage requirements are discussed. Limited angle tomography and non-traditional detection geometry may be handled using the described image reconstruction approach as well. The proposed method was tested with the list-mode PET data.