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Solution of linear equations in remote sensing and picture reconstruction

Lösung linearer Gleichungen in der Ferndeutung und Bilder-Rekonstruktion

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Abstract

The Moore-Penrose generalized inverse is utilized to obtain two general optimal solutions of a given system of linear equations. These solutions involve two matricesW andV. It is shown that available information regarding the desired solution and/or residual vector can be incorporated inW andV. Several of the known results in published literature are shown to be special cases of the optimal solutions given here.

Zusammenfassung

Es wird die Moore-Penrose generalisierte Inverse angewendet, um zwei allgemeine optimale Lösungen eines gegebenen Systems von linearen Gleichungen zu erhalten. Die Lösungen enthalten zwei MatrizenW undV. Es wird gezeigt, daß die vorhandene Auskunft in Bezug auf die gewünschte Lösung und/oder den verbleibenden Vektor inW undV einverleibt werden kann. Verschiedene Resultate in der Literatur sind somit Spezialfälle der hier gegebenen optimalen Lösungen.

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Authors and Affiliations

  1. Applied Mathematics and Statistics Department, State University of New York at Stony Brook, 11790, Stony Brook, NY, U.S.A.

    R. P. Tewarson

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  1. R. P. Tewarson
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Tewarson, R.P. Solution of linear equations in remote sensing and picture reconstruction. Computing 10, 221–230 (1972). https://doi.org/10.1007/BF02316909

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