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A block iterative algorithm for tomographic reconstruction of ionospheric electron density
Author(s) -
Sutton Eric,
Na Helen
Publication year - 1996
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/(sici)1098-1098(199623)7:3<238::aid-ima12>3.0.co;2-v
Subject(s) - a priori and a posteriori , algorithm , residual , weighting , tomographic reconstruction , iterative reconstruction , tomography , computer science , iterative method , block (permutation group theory) , reconstruction algorithm , mathematics , optics , computer vision , physics , geometry , philosophy , epistemology , acoustics
Ionospheric tomography is a technique whereby a vertical cross section through ionospheric electron density can be imaged. The vertical resolution of ionospheric tomography systems is inherently poor, but can be improved by using a priori information in the tomographic reconstruction algorithm. Care must be exercised in using a priori information, since if too much of it is used, the reconstruction algorithm may discard some of the information contained in the tomographic data in favor of satisfying some of the a priori assumptions. Orthogonal decomposition (OD) is an existing technique that uses a priori information to constrain the reconstruction to lie in a space of reasonable images without weighting the reconstruction toward any particular a priori image. In this way a priori information can be used in a manner that does not overwhelm information contained in the data. Gauss‐Seidel (GS) is an iterative algorithm that is used to calculate solutions for large systems of linear equations. In this article, a block version of the GS algorithm will be used to calculate the solution of the least‐squares problem that is created using OD. The complete algorithm presented here will be called the residual correction method (RCM), since it involves calculation of successively better approximations based on the residual error. RCM is a fast and numerically stable algorithm that extracts as much information from the data as possible. A numerical example demonstrating the properties of RCM will also be presented. © 1996 John Wiley & Sons, Inc.