Premium
Approximate inverse meets local tomography
Author(s) -
Rieder Andreas,
Dietz Rainer,
Schuster Thomas
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(200010)23:15<1373::aid-mma170>3.0.co;2-a
Subject(s) - mathematics , discretization , classification of discontinuities , convergence (economics) , tomography , inverse problem , inverse , algorithm , tomographic reconstruction , iterative reconstruction , mathematical optimization , mathematical analysis , computer science , geometry , artificial intelligence , physics , optics , economics , economic growth
Local or lambda tomography reconstructs Λƒ which has the same discontinuities as the searched‐for density distribution ƒ. Computing Λƒ, however, requires only local tomographic measurements. Local tomography is usually implemented by a filtered backprojection algorithm (FBA). In the present article we design reconstruction filters for the FBA such that Λ 2 m +1 ƒ will be reconstructed for a given m ∈ℕ 0 . Moreover, we 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 which yields a proper scaling of the reconstruction filters. Numerical experiments illustrate the analytic results. Copyright © 2000 John Wiley & Sons, Ltd.