  As computational tools for X-ray computed tomography (CT) become more
quantitatively accurate, knowledge of the source-detector spectral response is
critical for quantitative system-independent reconstruction and material
characterization capabilities. Directly measuring the spectral response of a CT
system is hard, which motivates spectral estimation using transmission data
obtained from a collection of known homogeneous objects. However, the
associated inverse problem is ill-conditioned, making accurate estimation of
the spectrum challenging, particularly in the absence of a close initial guess.
In this paper, we describe a dictionary-based spectral estimation method that
yields accurate results without the need for any initial estimate of the
spectral response. Our method utilizes a MAP estimation framework that combines
a physics-based forward model along with an $L_0$ sparsity constraint and a
simplex constraint on the dictionary coefficients. Our method uses a greedy
support selection method and a new pair-wise iterated coordinate descent method
to compute the above estimate. We demonstrate that our dictionary-based method
outperforms a state-of-the-art method as shown in a cross-validation experiment
on four real datasets collected at beamline 8.3.2 of the Advanced Light Source
(ALS).
