Everything about Radon transform
Integral transform in mathematics
In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line. The transform was introduced in 1917 by Johann Radon, who also provided a formula for the inverse transform. Radon further included formulas for the transform in three dimensions, in which the integral is taken over planes. It was later generalized to higher-dimensional Euclidean spaces and more broadly in the context of integral geometry. The complex analogue of the Radon transform is known as the Penrose transform. The Radon transform is widely applicable to tomography, the creation of an image from the projection data associated with cross-sectional scans of an object. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Radon transformA 5-minute orientation
- Skim a recent paper: The Modulo Radon Transform: Theory, Algorithms, and ApplicationsInfluential work since 2022
- Pick up a classic book: The Radon TransformThe most-reprinted book on the subject
- Read the landmark paper: Discrete radon transformCited 339 times
- Go sideways: Fractional LaplacianA closely related topic
- Go sideways: Cauchy waveletA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Discrete radon transform
The Exponential Radon Transform
Hough Transform from the Radon Transform
Sampling the 2-D Radon transform
3D Fourier based discrete Radon transform
The Interior Radon Transform
The discrete periodic Radon transform
Dispersive Radon transform
🆕 Influential since 2022
The Modulo Radon Transform: Theory, Algorithms, and Applications
Segmented Radon Fourier Transform for Long-Time Coherent Radars
Fourier-Domain Inversion for the Modulo Radon Transform
The 3D conical Radon transform for seismic signal processing
Improving receiver function imaging with high-resolution Radon transform
📚 Books worth reading
The Radon TransformSigurdur Helgason · 2013- 📕Radon Transform and Local TomographyAlexander G. Ramm, Alex I. Katsevich · 2020
- 📕Reconstruction from Integral DataVictor Palamodov · 2016
The Radon Transform and Some of Its ApplicationsStanley R. Deans · 1983- 📕Radon TransformRonny Ramlau, Otmar Scherzer · 2019
Mathematical methods in tomographyGabor T. Herman, F. Natterer · 1991
Integral geometry, radon transforms, and complex analysisCarlos A. Berenstein, Massimo A. Picardello · 1998
Kalibrovochnye poli︠a︡ i kompleksnai︠a︡ geometrii︠a︡Manin, I͡U. I. · 1984
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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