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Inversion Formulas for a Cylindrical Radon Transform
SIAM Journal on Imaging Sciences, 2011In this paper we study the inversion of a generalized Radon transform that maps a function in three dimensional space to a family of cylindrical integrals. We derive local backprojection-type inversion formulas for this cylindrical Radon transform. Our inversion formulas can be implemented in a straightforward manner with $\mathcal{O}(\mathtt{N}^{4/3})$
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An inversion formula for the Laplace transform
1992For real, right continuous and bounded functions \(f\) with Laplace transform \(\phi\) the inversion formula \[ f(x)= \lim_{\varepsilon\to +0} \lim_{\lambda\to \infty} {1\over \varepsilon} \sum_{\lambda x< k\leq \lambda(x+ \varepsilon)}(- 1)^ k {\lambda^ k\over k!} \phi^{(k)}(\lambda) \] is proved for \(x\geq 0\).
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On the inversion formula for probability densities
1997Let \(\varphi: \mathbb{R}^d \to\mathbb{C}\) be the characteristic function determined by a certain \(d\)-dimensional distribution function \(F:\mathbb{R}^d\to \langle 0,1 \rangle\subset \mathbb{R}\). Assuming that \(\varphi\) is square integrable, the author succeeds to derive from Lévy's inversion theorem a formula for the probability density of \(F\),
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A note on the stability of Toeplitz matrix inversion formulas
Applied Mathematics Letters, 2004Michael Ng, Wai-Ki Ching, Youwei Wen
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A family of inversion formulas in thermoacoustic tomography
Inverse Problems and Imaging, 2009Linh V Nguyen
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On the inversion formulas of Pestov and Uhlmann for the geodesic ray transform
Journal of Inverse and Ill-Posed Problems, 2010Venkateswaran Krishnan
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Some new convolution properties and inversion formulas of Laplace transforms
Integral Transforms and Special Functions, 2014L Debnath
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