Find the output of each PMT for a scintillation event that occurs at (−0.5, 0.5) cm.

Consider nine 1 cm × 1 cm PMTs arranged in 3 × 3 array (Figure P8.2). The output of each PMT to a scintillation event is modeled as

where (x, y) is the location of the scintillation event, and (xi, yi) is the center of the i-th PMT.

Figure P8.2 See Problem 8.8.

(a) Find the output of each PMT for a scintillation event that occurs at (−0.5, 0.5) cm.

(b) What is the estimated position of the scintillation event?

(c) Is the estimated position the same as its true position? If not, explain why

find the cost of your paper

Explain why attenuation is not a big problem in PET.

Consider a 2-D object consisting of two triangle compartments, as shown in Figure P9.4. Suppose a solution containing a 511 KeV gamma ray emitting radionuclide with concentration f = 0.5….

Give the mean and the variance of the reconstructed image, mean[ˆ f(x, y)] and var[ˆ f(x, y)].

Ignoring the inverse square law and attenuation, an approximate reconstruction for SPECT imaging is given by where c˜() =  {||W()} and W() is a rectangular windowing filter that cuts off at = 0…..

Find the numerical responses in each to an event in crystal C(4, 6).

Suppose a PET detector comprises four square PMTs (arranged as a 2 by 2 matrix) and a single BGO crystal with slits made in such a way that it is….