  In the Alvarez-Macovski method, the line integrals of the x-ray basis set
coefficients are computed from measurements with multiple spectra. An important
question is whether the transformation from measurements to line integrals is
invertible. This paper presents a proof that for a system with two spectra and
a photon counting detector, pileup does not affect the invertibility of the
system. If the system is invertible with no pileup, it will remain invertible
with pileup although the reduced Jacobian may lead to increased noise.
