  Dual energy computed tomography (DECT) imaging plays an important role in
advanced imaging applications due to its material decomposition capability.
Image-domain decomposition operates directly on CT images using linear matrix
inversion, but the decomposed material images can be severely degraded by noise
and artifacts. This paper proposes a new method dubbed DECT-MULTRA for
image-domain DECT material decomposition that combines conventional penalized
weighted-least squares (PWLS) estimation with regularization based on a mixed
union of learned transforms (MULTRA) model. Our proposed approach pre-learns a
union of common-material sparsifying transforms from patches extracted from all
the basis materials, and a union of cross-material sparsifying transforms from
multi-material patches. The common-material transforms capture the common
properties among different material images, while the cross-material transforms
capture the cross-dependencies. The proposed PWLS formulation is optimized
efficiently by alternating between an image update step and a sparse coding and
clustering step, with both of these steps having closed-form solutions. The
effectiveness of our method is validated with both XCAT phantom and clinical
head data. The results demonstrate that our proposed method provides superior
material image quality and decomposition accuracy compared to other competing
methods.
