gives the inverse Radon transform of expr.

Details and Options

• The inverse Radon transform provides the mathematical basis for tomographic image reconstruction.
• Geometrically, the inversion procedure recovers an image from the values of its Radon transform along different projections of the image for fixed angles and varying .
• InverseRadonTransform computes a radial Fourier transform, followed by a two-dimensional inverse Fourier transform, to accomplish the above inversion. »
• The following options can be given:
•  Assumptions \$Assumptions assumptions on parameters GenerateConditions False whether to generate results that involve conditions on parameters Method Automatic what method to use

Examples

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Basic Examples(1)

Compute the inverse Radon transform of a function:

Plot the function along with the inverse transform:

Scope(5)

Basic Uses(1)

Compute the inverse Radon transform of a function for symbolic parameter values:

Use exact values for the parameters:

Use inexact values for the parameters:

Gaussian Functions(2)

Inverse Radon transform of a Gaussian function:

Plot the function along with the inverse transform:

Polynomial Gaussian function:

Product of a polynomial Gaussian function with trigonometric functions:

Piecewise and Generalized Functions(2)

Inverse Radon transform of a piecewise function:

Inverse Radon transform of an expression involving DiracDelta:

Applications(2)

Compute the symbolic inverse Radon transform of a function:

Obtain the same result using InverseRadon:

Use the Radon transform to solve a Poisson equation:

Solve the ordinary differential equation using DSolveValue:

Set the arbitrary constants in the solution to 0:

Obtain the solution for the original equation using InverseRadonTransform:

Verify the solution:

Plot the solution:

Properties & Relations(3)

Compute the inverse Radon transform using Fourier transforms:

Find the Fourier transform with respect to p:

Express the result in terms of a unit vector ξ = { u1,u2}, assuming that :

Compute the inverse Fourier transform with respect to { u1,u2}:

Obtain the same result directly using InverseRadonTransform:

Neat Examples(1)

Create a table of inverse Radon transforms:

CMS

Wolfram Language. 2017. "InverseRadonTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseRadonTransform.html.