Numerically robust minimal-scan reconstruction algorithms for diffraction tomography via radon transform inversion

2002 ◽  
Vol 12 (2) ◽  
pp. 84-91 ◽  
Author(s):  
Mark A. Anastasio ◽  
Xiaochuan Pan
Keyword(s):  
Radon Transform ◽  
Diffraction Tomography ◽  
Reconstruction Algorithms

scholarly journals Recovering a Random Variable from Conditional Expectations Using Reconstruction Algorithms for the Gauss Radon Transform

2019 ◽  
pp. 1-31
Author(s):  
Jeremy Becnel ◽  
Daniel Riser-Espinoza
Keyword(s):  
Euclidean Space ◽  
Computerized Tomography ◽  
Radon Transform ◽  
Gaussian Measure ◽  
Random Variables ◽  
Random Variable ◽  
Dimensional Euclidean Space ◽  
Computer Implementation ◽  
Reconstruction Algorithms ◽  
Conditional Expectations

The Radon transform maps a function on n-dimensional Euclidean space onto its integral over a hyperplane. The fields of modern computerized tomography and medical imaging are fundamentally based on the Radon transform and the computer implementation of the inversion, or reconstruction, techniques of the Radon transform. In this work we use the Radon transform with a Gaussian measure to recover random variables from their conditional expectations. We derive reconstruction algorithms for random variables of unbounded support from samples of conditional expectations and discuss the error inherent in each algorithm.

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