Noniterative compensation for the distance-dependent detector response and photon attenuation in SPECT imaging

A filtering approach is described, which accurately compensates for the 2D distance-dependent detector response, as well as for photon attenuation in a uniform attenuating medium. The filtering method is based on the frequency distance principle (FDP) which states that points in the object at a specific source-to-detector distance provide the most significant contribution to specified frequency regions in the discrete Fourier transform (DFT) of the sinogram. By modeling the detector point spread function as a 2D Gaussian function whose width is dependent on the source-to-detector distance, a spatially variant inverse filter can be computed and applied to the 3D DFT of the set of all sinogram slices. To minimize noise amplification the inverse filter is rolled off at high frequencies by using a previously published Wiener filter strategy. Attenuation compensation is performed with Bellini's method. It was observed that the tomographic point response, after distance-dependent filtering with the FDP, was approximately isotropic and varied substantially less with position than that obtained with other correction methods. Furthermore, it was shown that processing with this filtering technique provides reconstructions with minimal degradation in image fidelity.