4. The tissue slice being imaged by a parallel beam x-ray CT scanner is shown in the figure below. (a) Assume the detector is a point detector. Sketch the projection g(1, @) as a function of /, for 0=0, 45, 90, and 135 degrees, respectively. You should indicate the magnitudes of the projected values where necessary on your sketch. Also any transition points in the horizontal axis. (b) Sketch the image obtained by back projections from both 0 and 90 degree projections. You should normalize your back projection using the dimension of the imaged region as indicated on the figure. (c) Determine the Fourier transform of the original image along a line with orientation 0=90 degree. 1 cm 1 gm 1 cm 6 cm U =1 cm- 1 cm in the target X 1 cm 4 =0cm 3 om at the background 6 cm