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To reconstruct a radioactive tracer distribution with positron emissiontomography (PET), the background attenuation correction is needed to eliminateimage artifacts. Recent research shows that time-of-flight (TOF) PET datadetermine the attenuation sinogram up to a constant, and its gradient can becomputed using an analytic algorithm. In this paper, we study a directestimation of the sinogram only from TOF PET data. First, the gradient of theattenuation sinogram is estimated using the aforementioned algorithm. Then, arelationship is established to link the differential attenuation sinogram andthe underlying attenuation background. Finally, an iterative algorithm isdesigned to determine the attenuation sinogram accurately and stably. A 2Dnumerical simulation study is conducted to verify the correctness of ourproposed approach.

Attenuation map reconstruction from TOF PET data