Estimation of gap data using bow-tie filters for 3D time-of-flight PET

In many PET scanners, there exist gaps between detector blocks and the data corresponding to lines of response associated with these gaps are missing. The missing gap data must be estimated prior to image reconstruction in cases where the sinogram data are rebinned into lower dimensional formats or when filtered backprojection (FBP) is used. Both bilinear interpolation and filters enforcing data consistency conditions have been used for non-TOF PET data. Here we develop a method for gap filling for TOF data by iteratively applying a bow-tie filter in the Fourier domain. We use a Fourier rebinning method (FORET-2D) to rebin the 3D TOF PET data to 2D non-TOF data and then apply bow-tie filtering to each of the stacked 2D sinograms. The estimated gap data are extracted from the 3D TOF sinograms computed by inverse rebinning from the bow-tie filtered 2D non-TOF data. The procedure can be repeated iteratively to further refine the gap estimates. Preliminary results indicate that the new method provides improved estimates of the gap data compared to bilinear interpolation and reduces artifacts due to interpolation error.