Retrieval of Asymmetric Temperature and Concentration Profiles From a Limited Number of Absorption Measurements

Abstract

—Established methods for obtaining the inverse of the Radon transform, the underlying reconstruction problem in the determination of asymmetric temperature and species concentration profiles from absorption measurements, are not well-suited for limited data problems. A new method that minimizes the number of measurements required by making use of a priori information such as the smoothness of the absorption coefficient profiles and constraints on its domain and range, has been applied to this inversion problem, Some free parameters, such as the choice of absorption frequencies and the use of shifting functions. that can be optimized to achieve improved reconstructions have been studied. Test results obtained by using simulated absorption measurements generated from phantom temperature and NO concentration distributions are presented. Comparison with the results obtained using the convolution backprojection method, a widely used method for solving the discrete data inverse Radon transform problem. is also included. It is found that the new method is superior to the convolution backprojection method.