The imaged slices incorporate noisy sample values of the Attenuated-Radon-Transform (ATRT) of f and mu. This is nonlinear in mu. Traditional SPECT reconstruction treats mu as known parameter. In practical applications, however, mu is not known, but crudely estimated or neglected.
We try to develop an algorithm that approximates both f and mu from SPECT data alone, in order to obtain quantitatively accurate SPECT images.
It combines Tikhonov regularization developed for nonlinear parameter estimation in partial differential equations and an adapted Gauss-Newton-CG minimization.
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