Three-dimensional PET Reconstruction with Time-of-flight Measurement

The interest in fully three-dimensional image reconstruction, especially in positron emission tomography (PET) has significantly increased for the last few years. Taking into account the cross-plane gamma rays in a three-dimensional reconstruction algorithm improves the sensitivity. At LETI, our specialty in PET is the time-of-flight (TOF) measurement. Thus, we present in this article two reconstruction techniques for 3D TOF PET. The first is a backprojection-convolution algorithm. Due to the redundancy in the 3D data set, there exists an infinite number of filters. As Defrise and co-workers did for classical tomography, we established a general condition that characterizes the filters and propose an algorithm with a factorizable filter. However, this first technique requires an acquisition system with revolution symmetry. Thus, we present a second one which is adapted to a detection geometry with a small number of angular positions. It consists of a multi-image deconvolution algorithm with Wiener filter.