The time-of-flight (TOF) information makes Orlov's condition not necessary for positron emission tomography (PET) imaging. One-view imaging has never been attempted before. This paper investigates whether one-view imaging is possible. We claim that it is possible to obtain an image with measurements from only one-view, provided the TOF time resolution is good enough and the photon counts are high enough. In fact, the image value at a point can be reconstructed by measurements along one line-of-response (LOR) that passes through the point of interest. The region-of-interest (ROI) can be reconstructed with ray-by-ray deblurring methods, which make TOF PET a local tomography system. One-view imaging is a severely ill-posed problem if the TOF resolution is not good enough. One indicator of an ill-posed problem is the ringing artifacts in the reconstruction. We show that ringing artifacts can be eliminated by using the nonnegativity constraint for the dot-like objects with a zero background.
Keywords: Positron emission tomography; analytic reconstruction; local tomography; nonnegativity constrained reconstruction; time-of-flight.