HYBRID POISSON POLYNOMIAL OBJECTIVE FUNCTIONS FOR TOMOGRAPHIC IMAGE-RECONSTRUCTION FROM TRANSMISSION SCANS

This paper describes rapidly converging algorithms for computing attenuation maps from Poisson transmission measurements using penalized-likelihood objective functions. We demonstrate that an under-relaxed cyclic coordinate-ascent algorithm converges faster than the convex algorithm of Lange [1], which in turn converges faster than the expectation-maximization (EM) algorithm for transmission tomography [1], To further reduce computation, one could replace the log-likelihood objective with a quadratic approximation, However, we show with simulations and analysis that the quadratic objective function leads to biased estimates for low-count measurements, Therefore we introduce hybrid Poisson/polynomial objective functions that use the exact Poisson log-likelihood for detector measurements with low counts, but use computationally efficient quadratic or cubic approximations for the high-count detector measurements. We demonstrate that the hybrid objective functions reduce computation time without increasing estimation bias.