I understand the Radon Transform get the product between the length(intersection) of each beam through the pixel and the pixel value (Proj=Area_intersection*pixel_value)
So, no, the radon transform is fundamentally a continuous-space operation. It is the integral through the continuous-space object along various lines. There are no "pixels" in a continuous-space operation.
What you have described is one way of discretizing the line integrals done by the radon transform when you have a pixelized object. It is the discretization used, for example, in Siddon's algorithm.
RL Siddon, "Fast calculation of the exact radiological path for a three-dimensional CT array". Med Phys. 2005
However, it is not the only way to discretize the Radon transform and not the method that Matlab's radon() command uses. Essentially, radon uses an approximate forward projection that is the transpose of the backprojection (minus the filtering) done by iradon.
What refer to 4 subpixels? How can I divide 1 pixel into 4 ??
It is not to be done by you. It is done internally by radon(). Basically, radon does a 2x2 upsampling of the input image before doing the forward projection. It is meant simply to get a less coarse forward projection result.