An algorithm for real-time tomography of gas concentrations, using prior information about spatial derivatives

We present a new computed tomography method, the low third derivative (LTD) method, that is particularly suited for reconstructing the spatial distrib ution of gas concentrations from path-integral data for a small number of o ptical paths. The method finds a spatial distribution of gas concentrations that (1) has path integrals that agree with measured path integrals, and ( 2) has a low third spatial derivative in each direction, at every point. Th e trade-off between (1) and (2) is controlled by an adjustable parameter, w hich can be set based on analysis of the path-integral data. The method pro duces a set of linear equations, which can be solved with a single matrix m ultiplication if the constraint that all concentrations must be positive is ignored; the method is therefore extremely rapid. Analysis of experimental data from thousands of concentration distributions shows that the method w orks nearly as well as smooth basis function minimization (the best method previously available), yet is about 100 times faster. (C) 2001 Published by Elsevier Science Ltd.