A back‐projection‐and‐filtering‐like (BPF‐like) reconstruction method with the deep learning filtration from listmode data in TOF‐PET

Abstract Purpose The time‐of‐flight (TOF) information improves signal‐to‐noise ratio (SNR) for positron emission tomography (PET) imaging. Existing analytical algorithms for TOF PET usually follow a filtered back‐projection process on reconstructing images from the sinogram data. This work aims to develop a back‐projection‐and‐filtering‐like (BPF‐like) algorithm that reconstructs the TOF PET image directly from listmode data rapidly. Methods We extended the 2D conventional non‐TOF PET projection model to a TOF case, where projection data are represented as line integrals weighted by the one‐dimensional TOF kernel along the projection direction. After deriving the central slice theorem and the TOF back‐projection of listmode data, we designed a deep learning network with a modified U‐net architecture to perform the spatial filtration (reconstruction filter). The proposed BP‐Net method was validated via Monte Carlo simulations of TOF PET listmode data with three different time resolutions for two types of activity phantoms. The network was only trained on the simulated full‐dose XCAT dataset and then evaluated on XCAT and Jaszczak data with different time resolutions and dose levels. Results Reconstructed images show that when compared with the conventional BPF algorithm and the MLEM algorithm proposed for TOF PET, the proposed BP‐Net method obtains better image quality in terms of peak signal‐to‐noise ratio, relative mean square error, and structure similarity index; besides, the reconstruction speed of the BP‐Net is 1.75 times faster than BPF and 29.05 times faster than MLEM using 15 iterations. The results also indicate that the performance of the BP‐Net degrades with worse time resolutions and lower tracer doses, but degrades less than BPF or MLEM reconstructions. Conclusion In this work, we developed an analytical‐like reconstruction in the form of BPF with the reconstruction filtering operation performed via a deep network. The method runs even faster than the conventional BPF algorithm and provides accurate reconstructions from listmode data in TOF‐PET, free of rebinning data to a sinogram.