Approximate inverse meets local tomography

Local or lambda tomography reconstructs Lambda f which has the same discont inuities as the searched-for density distribution f. Computing Lambda f, ho wever, requires only local tomographic measurements. Local tomography is us ually implemented by a filtered backprojection algorithm (FBA). In the pres ent article we design reconstruction filters for the FBA such that Lambda(2 m+1)f will be reconstructed for a given m is an element of N-0. Moreover, w e prove convergence and convergence rates for the FBA as the discretization step size goes to zero. To this end we express the FBA in the framework of approximate inverse. Based on our analysis we further propose a scheme whi ch yields a proper scaling of the reconstruction filters. Numerical experim ents illustrate the analytic results. Copyright (C) 2000 John Wiley & Sons, Ltd.