To create a simulated phantom sinogram, it is common to firstly create the 2-d digital image: I = phantom(xxx), and then apply the radon() transform: R = radon(I, theta).
Since the phantom image has its analytical expression, it will be more accurate to simulate the parallel projection if the radon transform is performed on the analytical expression. In page 52 of the textbook "Principles of Computerized Tomographic Imaging", there has been such comment "a major advantage of using an image like that in Fig. 3.4(a) for computer simulation is that now one can write analytical expressions for the projections."
Is it possible in Matlab?
This is tricky...you have to write your own matlab script to do this.
since the phantom is basically the sum of some coefficients times a Chi functions on different ellipses,
f(x)=sum_i c_i Chi(x,E_i)
with Chi(x,E) = 1 if x is in the ellipse E, 0 otherwise
so the radon transform in (t,theta) should be the sum of length of the intersection between the line (t,theta) and the i-th ellipse times the coefficients c_i
Rf(t,theta)=sum_i c_i L_i(t,theta)
with L_i the length of intersection.
Personally, I will not try to this.
I consider the "radon" function pretty accurate, the problems arrive when using the inverse function "iradon".
thank you very much.
then, I have tried to implement the analytical expression, and the results are shown as follows.
this looks interesting, thank you for posting the images!
what is the error (say 2-norm or inf-norm) between the analytical sinogram and the one obtained with "radon" function?
please consider publish the code via github/matlabcentral
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