Correction of the DDRV in fan-beam SPECT reconstruction

In SPECT, in order to achieve a useful sensitivity, the aperture of collimator hole cannot be reduced to zero. This nonzero aperture results in distance-dependent resolution variation (DDRV) in the acquired projection data and in the reconstructed images. Based on the special characteristics of the Fourier coefficients of sinogram, Lewitt proposed a method that can correct the DDRV of the parallel-beam projection in frequency domain. For clinical applications, fan-beam collimators would be preferred for brain and chest imaging, which can improves count density and spatial resolution for imaging small objects. In this case, someone needs to rebin the fan-beam sinogram to the parallel-beam sinogram, and then use Lewitt´s method to correct the DDRV in frequency domain. In this work, we propose a new method for the DDRV correction of fan-beam SPECT projection, which doesn´t need rebinning, can obtain the Fourier coefficients of parallel-beam projection from the fan-beam projection data directly.