gives the Radon transform of expr.

# Details and Options • The Radon transform of a function is defined to be .
• Geometrically, the Radon transform represents the integral of along a line given in normal form by the equation , with -<p< and -π/2<ϕ<π/2.
• • 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
• In TraditionalForm, RadonTransform is output using .

# Examples

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## Basic Examples(1)

Compute the Radon transform of a function:

Plot the function along with the transform:

## Scope(10)

### Basic Uses(2)

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

Use exact values for the parameters:

Use inexact values for the parameters:

Obtain the condition for validity of a Radon transform:

Specify assumptions:

### Gaussian Functions(5)

Radon transform of a circular Gaussian function:

Plot the function along with the transform:

Radon transform of an elliptic Gaussian function:

Plot the function along with the transform:

Product of a polynomial with a Gaussian function:

Product of Hermite polynomials and a Gaussian function:

Products of trigonometric functions with Gaussian functions:

### Piecewise and Generalized Functions(3)

Radon transform of the characteristic function for the unit disk:

Products of polynomials with the characteristic function for the unit disk:

Radon transforms for expressions involving DiracDelta:

## Options(2)

### Assumptions(1)

Specify assumptions:

### GenerateConditions(1)

Generate conditions for the validity of the result:

## Applications(2)

Compute the symbolic Radon transform for the characteristic function of a disk:

Obtain the same result using Radon:

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(10)

RadonTransform computes the integral :

Obtain the same result using Integrate:

Express the Radon transform of in terms of a unit vector:

Verify the symmetry property:

Express the Radon transform of in terms of a unit vector:

Verify the homogeneity property:

Express the Radon transform of in terms of a unit vector:

Express the Radon transform of in terms of a unit vector:

Verify the scaling property:

RadonTransform can be computed using Fourier transforms:

Compute the Fourier transform of f in polar coordinates:

Compute the inverse Fourier transform to obtain the Radon transform:

Obtain the same result directly using RadonTransform:

## Neat Examples(1)

Create a table of basic Radon transforms:

Introduced in 2017
(11.2)