Off-axis multi-slit coding for tomographic x-ray imaging of microplasma

Beaucoudrey, N. de; Garnero, Line

doi:10.1016/0030-4018(84)90371-7

Cited by 6 publications

(2 citation statements)

References 5 publications

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“…Sometimes the code function C is approximated by distributional measures, so that the scope of the RTC is enlarged: In [1] or [24] authors use regular grids of pinholes (modeled by ponctual Dirac δ measures). Systems of rectilign slits, as in [11] and [15], are also studied (and even stochastic apertures in [22]). Pinholes lead to the "divergent-beam transform" ( [23]), and rectilign slits lead to the usual radon transform over hyperplanes.…”

Section: 22mentioning

confidence: 99%

Radon Transform over Cones and Related Deconvolution Problems

Crouzet¹

2001

J. Integral Equations Applications

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We introduce a new kind of radon transform, consisting in integrating a function (to be recovered) over a special family of cones. It is in fact a formal generalization of the "Coded-aperture gammagraphy" imaging method, encountered in medicine and astronomy. We show that it is a natural geometric operation, but which does not have the fine properties of similar integral transform. Nevertheless, several inverse problems (like classical radon transform, deconvolution) are related to it, and also new kinds on integral transforms : essentially the "Quasi-convolution". After this study, where we show that the problem is severely ill-posed (essentially because of insufficient data), an inversion is performed in the case of complete data.

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Section: 22mentioning

confidence: 99%

Radon Transform over Cones and Related Deconvolution Problems

Crouzet¹

2001

J. Integral Equations Applications

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“…If C is the indicator function of the hole, then the image on the screen is given by the formula Sometimes the code is a small ring-shaped hole (see [2,4,5]) or a system of concentric ring-shaped holes (called Fresnel zones). It is possible to choose, similarly to [6], regular grids of needle-shaped holes or systems of rectilinear cross-cuts as in [3]. Below we investigate a special class of holes that permits reconstruction of the density.…”

Section: W Recognition Of Images In Medicine and A Quasi-convolutionmentioning

confidence: 99%