Accurate Attenuation Correction in SPECT Imaging Using Optimization of Bilinear Functions and Assuming an Unknown Spatially-Varying Attenuation Distribution

Abstract

We report on an iterative approach to reconstruct both the activity f(x) and the attenuation μ(x) directly frorn the emission sinogram data. The proposed 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 operator, a modified iteration sequence can be defined. Using a Taylor series about a fixed approximate distribution μ 0 , the attenuated Radon transform can be well approximated as the sum of a linear operator in f and a bilinear operator in f and μ. The algorithm alternates between updates of f and updates of μ. In our test computations, the proposed algorithms achieve good reconstruction results both for generated and real data.