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• W1519197923 abstract "Publisher Summary Singular Value Decompositions have proved very useful in getting efficient solvers for linear inverse problems. Regularized solutions can be computed as filtered expansions on singular system of the integral operator to be inverted. In a few special instances of interest in optical imaging, this chapter shows that the relevant singular systems exhibit a series of nice analytic properties. The chapter first considers the inversion of a finite Laplace transform, that is of a Laplace transform where the solution or the data have finite support. The corresponding singular functions are shown to be also the eigenfunctions of a second-order differential operator closely related to the Legendre operator. This remarkable fact allows to derive further properties, which are similar to some well-known properties of the prolate spheroidal wave functions. The second compact linear integral operator that is considered in this chapter describes the one-dimensional coherent imaging properties of a confocal microscope. Its singular functions have very simple analytic expressions and, the determination of the generalized inverse of this integral operator reduces to the inversion of an infinite matrix whose inverse can also be derived analytically." @default.
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• W1519197923 date "1995-01-01" @default.
• W1519197923 modified "2023-09-23" @default.
• W1519197923 title "SVD for linear inverse problems" @default.
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• W1519197923 doi "https://doi.org/10.1016/b978-044482107-2/50035-2" @default.
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