Masahiro MIMURA,^1,2 Takashi OBI,^1,* Masahiro YAMAGUCHI¹ and Nagaaki OHYAMA¹

¹Imaging Science and Engineering Laboratory, Tokyo Institute of Technology, 4259, Nagatsuta, Midori-ku, Yokohama, 226-8503 Japan, ²Cancer Information and Epidemiology Division, National Cancer Center Research Institute, 5-1-1, Tsukiji, Chuo-ku, Tokyo, 104-0045 Japan

(Received December 22, 1997; Accepted June 16, 1998)

The single photon emission computed tomography (SPECT) imaging system has shift-variant characteristics due to non-uniform attenuation of gamma-ray, collimator design, scattered photons, etc. In order to provide quantitatively accurate SPECT images, these characteristics should be compensated in the reconstruction. This paper presents a new method to correct the shift-variant characteristics, which is based on a continuous-discrete mapping model and filtered backprojection (FBP) method, in which the projection data are assumed to be acquired by narrow ray sum beams in the FBP method and the assumed data set is expressed as a linear combination of the actual projection data. Narrow ray sum beams are approximated by a weighted sum of the original sensitivity functions. Thus, at the reconstruction the projection data are first modified using an approximation and the FBP method is then applied to the corrected projection data and a SPECT image is reconstructed. We further propose a technique that requires the inversion of smaller matrices than the conventional algebraic method; the amount of calculation and memory space become smaller and the stability of the calculation is greatly improved as well. The results of the numerical simulations are also demonstrated.

Key words : SPECT imaging, non-uniform attenuation, sensitivity function, filtered backprojection, natural pixel decomposition, Continuous-Discrete mapping model, numerical, algebraic reconstruction, fast calculation

* obi@isl.titech.ac.jp