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Accurate Attenuation Correction in SPECT Imaging Using Optimization of Bilinear Functions and Assuming an Unknown Spatially‐Varying Attenuation Distribution
Author(s) -
Ramlau R.,
Clackdoyle R.,
Noo F.,
Bal G.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200009)80:9<613::aid-zamm613>3.0.co;2-9
Subject(s) - bilinear interpolation , attenuation , operator (biology) , algorithm , iterative method , mathematics , computation , distribution (mathematics) , linear map , sequence (biology) , taylor series , radon transform , mathematical optimization , mathematical analysis , physics , optics , pure mathematics , biochemistry , statistics , chemistry , genetics , repressor , biology , transcription factor , gene
We report on an iterative approach to reconstruct both the activity f ( x ) and the attenuation μ ( x ) directly from 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.