A Kalman filtering approach to stochastic tomography

An isotropic random field is expanded into its circular harmonics. Computation of its Radon transform is equivalent to computation of the n^th-order Abel transform of the n^th order circular harmonic. A state-space model is fitted to the Abel transform of each order and augmented with a state-space model describing the random field circular harmonic. The latter is derived using backward Markovianization of a two-point boundary value model. The tomographic problem of computing the inverse Radon transform is then solved by using a bank of Kalman filters to estimate each random field harmonic separately. Combining these gives the linear least-squares estimate of the random field. The authors also consider a simpler Wiener process model of the circular harmonics