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

Reports on an iterative approach to reconstruct the activity f(x) directly from the emission sinogram data without additional transmission measurements. The proposed algorithm is based on iterative methods for solving linear operator equations. When 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 μ₀, 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. Test computations for generated and real data show that the authors´ reconstructions achieve the same quality as reconstructions with known attenuation distribution