1. 2. Consider the "unit square function" given by f(x, y) = {1, −1 ≤ x ≤ 1, −1 ≤ y ≤ 1 otherwise Let p(r, 0) be the 2D Radon transform of ƒ (x, y). (a) Determine p(r, 0). (b) Determine p(r,ï/4). A first generation CT scanner is used to image a unit-square shaped object (i.e., length of each side = 1). The object is surrounded by air and has a constant linear attenuation coefficient of μ. The coordinate system is set up such that the origin is at the object center, and the x- and y-axes are parallel to the sides of the object. (a) (4 pts) Write a mathematical expression for the linear attenuation function (x, y). (Hint: Use the rect function) (b) (4 pts) Determine the Fourier transform of μ(x, y). (c) (5 pts) Determine p(r,0°) using the definition of Radon transform. (d) (5 pts) Determine P(K,0°) using projection-slice theorem. (e) (5 pts) Determine p(r,0°) by taking the inverse Fourier transform of P(K,0°). Compare your result with that from part (c). (f) (5 pts) Determine b (x, y) from p(r,0°).