1. Radon transform and central slice theorem. (a) An alternative way to write the Radon transform is using the delta function: P f(x,y)8(xcos 9+ y sin o-r)dxdy Verify that this is equivalent to p.(r)=[ f(r+st)ds. (Hint: change coordinates from (x, y) to (r,s).) (b) Use the Radon transform in equation (*) to verify the central slice theorem. (Hint: what is the Fourier transform of a shifted delta function?) 1. x2 (c) Find the Radon transform of an ellipse f(x, y) = {"; 4* , 10, otherwise (d) MATLAB: create a digital image of f(x,y) in (c) and calculate its Radon transform numerically. Example code: pixelsize = 0.1; t = [-2:pixelsize:2]; [x, y] = meshgrid(t); f=(x.*x/4+y. *y