Nonuniform Depth Distribution Selection with Discrete Fourier Transform

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Mapping 2-D defects in a conductive half-space by eigenfunction expansions in K-space of Fourier-Laplace transforms

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Superresolution: an ill-posed problem in Fourier optics

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On the regularization of linear inverse problems in Fourier optics

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Linear inverse problems with discrete data: II. Stability and regularization

For pt.I. see ibid. vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems has been performed. The problem of the numerical stability of the solution, which in that paper was only briefly discussed, is the main topic of this second part. When the condition number of the problem is too large, a small error on the data can produce an extremely large error on the generalised solution, which therefore has no physical meaning. The authors review most of the methods which have been developed for overcoming this difficulty, including numerical filtering, Tikhonov regularisation, iterative methods, the Backus-Gilbert method and so on. Regularisation methods for the stable approximation of generalised solutions obtained through minimisation of suitable seminorms (C-generalised solutions), such as the method of Phillips (1962), are also considered.

New high-resolution analysis of the ν7 and ν9 fundamental bands of trans-formic acid by IR Fourier transform and millimeterwave spectroscopies

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Laboratory Fourier transform spectroscopy of the water absorption continuum from 2500 to 22500 cm-1

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