A new approach towards simultaneous activity and attenuation reconstruction in emission tomography

In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the tissue density mu. Each imaged slice incorporates noisy sample values of the nonlinear attenuated Radon transform A(f, mu)(omega, s) = integral(-infinity)(infinity) f(s omega(perpendicular to) + t omega) exp (-integral(t)(infinity) mu(s omega(perpendicular to) + tau omega) d tau) dt. (1) Traditional theory for SPECT reconstruction treats mu as a known parameter. In practical applications, however, mu is not known, but either crudely estimated, determined in costly additional measurements or plainly neglected. We demonstrate that an approximation of both f and mu from SPECT data alone is feasible, leading to quantitatively more accurate SPECT images. The result is based on nonlinear Tikhonov regularization techniques for parameter estimation problems in differential equations combined with Gauss-Newton-CG minimization.