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…..

## 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 mCi/cm3 fills the lower triangle. The linear attenuation coefficients in the two regions are μ_{1} = 0.1 cm^{−1} and μ_{2} = 0.2 cm^{−1}. Assume perfect detection in all cases and ignore the inverse square law effect.

(a) We image the radioactivity using a 2D SPECT scanner. Compute the projected radioactivities gSPECT(, 0◦) and gSPECT(, 180◦). The camera is located on the +y-axis looking down when θ = 0◦.

(b) Now assume the radionuclide in part (a) is replaced by a positron emitting radionuclide with the same concentration. Assume the linear attenuation coefficients in the two regions are the same as in part (a). If using a 2D PET scanner, compute gPET(, 0◦) and gPET(, 180◦).

(c) Explain why attenuation is not a big problem in PET.

Figure P9.4 An object with triangular compartments. See Problem 9.4.