  Accurate reconstruction of 2D and 3D isotope densities is a desired
capability with great potential impact in applications such as evaluation and
development of next-generation nuclear fuels. Neutron time-of-flight (TOF)
resonance imaging offers a potential approach by exploiting the characteristic
neutron absorption spectra of each isotope. However, it is a major challenge to
compute quantitatively accurate images due to a variety of confounding effects
such as severe Poisson noise, background scatter, beam non-uniformity,
absorption non-linearity, and extended source pulse duration.
  We present the TRINIDI algorithm which is based on a two-step process in
which we first estimate the neutron flux and background counts, and then
reconstruct the areal densities of each isotope and pixel. Both components are
based on the inversion of a forward model that accounts for the highly
non-linear absorption, energy-dependent emission profile, and Poisson noise,
while also modeling the substantial spatio-temporal variation of the background
and flux. To do this, we formulate the non-linear inverse problem as two
optimization problems that are solved in sequence. We demonstrate on both
synthetic and measured data that TRINIDI can reconstruct quantitatively
accurate 2D views of isotopic areal density that can then be reconstructed into
quantitatively accurate 3D volumes of isotopic volumetric density.
