Topics:
The homework has four consecutive parts. When completed, you will have your own implementation of the forward projection ( Radon transform) used in CT imaging. A set of projections with varying direction $\theta$ is acquired. The object Cartesian coordinate system (grid) is denoted $x, y$. We shall also define a rotated coordinate system $p$, $q$, chosen so that projection corresponds to integration along the $p$ axis, creating a 1D function of $q$ for each angle $\theta$. Illustration of both coordinate systems is given below:
(Implementing our own Radon transform will help us to understand the inverse transform, which is the key concept for image reconstruction from measured CT projections. This will be the topic of the next lab.)
Homework tasks
function fwrad = myRadon(img, theta)which will return the forward Radon transform
fwrad
of the input image img
of dimension $[m \times n]$, given the array of projections angles theta
of length $k$ (angles are provided in degrees). Size of the resulting sinogram fwrad
is $[(2p_m + 1) \times k]$. Submit the code into BRUTE.
Hints
fwrad
sinogram.