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 (integrating over lines is known as the X-ray transform). 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.
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Filtered back projection in the context of Iterative reconstruction
Iterative reconstruction refers to iterative algorithms used to reconstruct 2D and 3D images in certain imaging techniques.For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are usually abetter, but computationally more expensive alternative to the common filtered back projection (FBP) method, which directly calculates the image ina single reconstruction step. In recent research works, scientists have shown that extremely fast computations and massive parallelism is possible for iterative reconstruction, which makes iterative reconstruction practical for commercialization.
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