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

A filtering approach is described which accurately compensates for the 2-D distance-dependent detector response, as well as for photon attenuation in a uniform attenuating medium. The filtering method is based on the energy distance principle (EDP), 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 2-D Gaussian function whose width is dependent on the source-to-detector distance, a spatially variant inverse filter can be computed and applied to the 3-D 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 EDP, was approximately isotropic and varied substantially less with position than that obtained with other correction methods