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Radon Transform
Fouad Sabry
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Naturwissenschaften, Medizin, Informatik, Technik / Informatik, EDV
Beschreibung
What is Radon Transform
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.
How you will benefit
(I) Insights, and validations about the following topics:
Chapter 1: Radon transform
Chapter 2: Fourier transform
Chapter 3: Bessel function
Chapter 4: Convolution theorem
Chapter 5: Discrete Fourier transform
Chapter 6: Fourier series
Chapter 7: Integration by parts
Chapter 8: Fractional Fourier transform
Chapter 9: Mellin transform
Chapter 10: Poisson kernel
(II) Answering the public top questions about radon transform.
(III) Real world examples for the usage of radon transform in many fields.
Who this book is for
Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Radon Transform.
Kundenbewertungen
Integration by parts, Discrete Fourier transform, Fourier transform, Fourier series, Radon transform, Convolution theorem, Bessel function