A CT system is designed to acquire M parallel-ray projections of f (x, y) at angles The...

A CT system is designed to acquire M parallel-ray projections of f (x, y) at angles The collection of projections measured by this system (modeled to be continuous in is defined to be the M-projection Radon transform:

(a)Draw a picture showing the four positions of the detector array required to determine Label which projection is acquired at each position.

(b) Knowledge of gives partial knowledge of the Fourier transform

(e) The result of part (c) means that you can add a function to the original without changing its M-projection Radon transform. In this context, such functions are called a ghost functions. In theory, is it possible to make M large enough so that there are no ghost functions of Explain your answer. What happens in practice?

(f) Suppose one used large detectors, effectively low-pass filtering each projection upon observation. Would still be a ghost function? Explain.