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iradon uses the filtered back projection algorithm to perform the inverse Radon transform. The filter is designed directly in the frequency domain and then multiplied by the FFT of the projections.
- Para2fan
F = para2fan(P,D) converts the parallel-beam data P to the...
- Radon
The Radon transform is the projection of the image intensity...
- Phantom
P = phantom(def,n) generates an image of a head phantom that...
- Ifanbeam
Algorithms. ifanbeam converts the fan-beam data to parallel...
- Theta
I =...
- Transformada de Radon inversa
iradon utiliza el algoritmo de retroproyección filtrada para...
- Para2fan
iradon utiliza el algoritmo de retroproyección filtrada para realizar la transformada de Radon inversa. El filtro se diseña directamente en el dominio de la frecuencia y luego se multiplica por la FFT de las proyecciones.
The iradon function inverts the Radon transform and can therefore be used to reconstruct images. As described in Radon Transform, given an image I and a set of angles theta, the radon function can be used to calculate the Radon transform.
- Create Head Phantom
- Parallel Beam - Calculate Synthetic Projections
- Parallel Beam - Reconstruct Head Phantom from Projection Data
- Fan Beam - Calculate Synthetic Projections
- Fan Beam - Reconstruct Head Phantom from Projection Data
The test image is the Shepp-Logan head phantom which can be generated using the function phantom. The phantom image illustrates many qualities that are found in real-world tomographic imaging of human heads. The bright elliptical shell along the exterior is analogous to a skull and the many ellipses inside are analogous to brain features or tumors.
Calculate synthetic projections using parallel-beam geometry and vary the number of projection angles. For each of these calls to radon, the output is a matrix in which each column is the Radon transform for one of the angles in the corresponding theta. Note that for each angle, the projection is computed at N points along the xp-axis, where Nis a ...
Match the parallel rotation-increment, dtheta, in each reconstruction with that used above to create the corresponding synthetic projections. In a real-world case, you would know the geometry of your transmitters and sensors, but not the source image, P. The following three reconstructions (I1, I2, and I3) show the effect of varying the number of a...
Calculate synthetic projections using fan-beam geometry and vary the 'FanSensorSpacing'. Display the projection data F3. Notice that the fan rotation angles range from 0 to 360 degrees and the same patterns occur at an offset of 180 degrees because the same features are being sampled from both sides. You can correlate features in this image of fan-...
Match the fan-sensor-spacing in each reconstruction with that used to create each of the synthetic projections. In a real-world case, you would know the geometry of your transmitters and sensors, but not the source image, P. Changing the value of the 'FanSensorSpacing'effectively changes the number of sensors used at each rotation angle. For each o...
La transformada de Radon es la proyección de la intensidad de la imagen a lo largo de una línea radial orientada en un ángulo determinado. ejemplo. R = radon(I,theta) devuelve la transformada de Radon para los ángulos que especifica theta.
The iradon function performs the inverse Radon transform, which is commonly used in tomography applications. This transform inverts the Radon transform (which was introduced in the previous section), and can therefore be used to reconstruct images from projection data.
The Radon transform is the projection of the image intensity along a radial line oriented at a specific angle. example. R = radon(I,theta) returns the Radon transform for the angles specified by theta. [R,xp] = radon( ___) returns a vector xp containing the radial coordinates corresponding to each row of the image.
