Accurate attenuation correction in SPECT imaging using optimization of bilinear functions and assuming an unknown spatially-varying attenuation distribution

We report on an iterative approach to reconstruct both the activity f(x) an d the attenuation mu(x) directly from the emission sinogram data. The propo sed algorithm is based on the iterative methods for solving linear operator equations. Whenever an operator F is the sum of a linear and a bilinear op erator, a modified iteration sequence can be defined. Using a Taylor series about a fixed approximate distribution mu(0), the attenuated Radon transfo rm can be well approximated as the sum of a linear operator in f and a bili near operator in f and mu. The algorithm alternates between updates of f an d updates of mu. In our test computations, the proposed algorithms achieve good reconstruction results both for generated and real data. MSC (1991): 6 5J10, 65D15.