Abstract
We outline a general procedure for reconstructing images and certain features from measurements based on a linear model. Roughly speaking, the method involves the construction of a Hilbert space on which the measurement functionals are continuous; the desired quantities can then be determined by variants of established techniques. In certain cases this construction results in a reproducing kernel Hilbert space. The basic ideas are illustrated by familiar examples, including certain models in tomography.
In short, the primary goal of this paper is to indicate a natural framework for the application of classical Hilbert space methods to the problem of reconstruction of images from indirect measurements.
Department of Mathematics, U-9; University of Connecticut; Storrs, CT 06269. Partially supported by a grant from the Air Force Office of Scientific Research, AFOSR-90-0311
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© 1991 Springer-Verlag Berlin Heidelberg
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Madych, W.R. (1991). Image reconstruction in Hilbert space. In: Herman, G.T., Louis, A.K., Natterer, F. (eds) Mathematical Methods in Tomography. Lecture Notes in Mathematics, vol 1497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084505
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DOI: https://doi.org/10.1007/BFb0084505
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