Monday, March 20, 2023

Radon transform by Johann Radon

The Radon transform is named after the Austrian mathematician Johann Karl August Radon (December16, 1887 – May 25, 1956). The Radon transform is an integral transform whose inverse is used to reconstruct images from medical CT scans.

Radon transform is able to transform two dimensional images with lines into a domain of possible line parameters, where each line in the image will give a peak positioned at the corresponding line parameters. This have led to many line detection applications within image processing, computer vision, and seismic.

A technique for using Radon transforms to reconstruct a map of a planet's polar regions using a spacecraft in a polar orbit has also been devised. The Radon Transformation is also used in various applications such as radar imaging, geophysical imaging, nondestructive testing and medical imaging.

Johann Radon had a remarkable career in mathematics: he was awarded a doctorate from the University of Vienna in Philosophy (for a thesis in the field of calculus of variations) in 1910.

After professorships in Hamburg, Greifswald, Erlangen, Breslau, and Innsbruck, he returned to the University of Vienna, where he became dean and later president of the University of Vienna.

In 1917, Johann Radon published his fundamental work, where he introduced what is now called the Radon transform. He presented a solution to the reconstruction problem with the Radon transform and its inversion formula. He developed this solution after building on the work of Hermann Minkowski and Paul Funk.

His work went largely unnoticed until 1972 when Allan McLeod Cormack and Arkady Vainshtein declared its importance to the field. Johann Radon is well-known for his ground-breaking achievements in mathematics, such as the Radon-transformation, the Radon-numbers, the theorem of Radon, the theorem of Radon–Nikodym and the Radon–Riesz theorem.
Radon transform by Johann Radon

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