  Purpose: This study proposes a systematic method for determining the optimal
x-ray tube settings/energy windows and fluence for minimal noise and maximum
CNR in material density images obtained from DECT scans by fixing the subject
size and the total radiation dose. Methods: The noise propagation in the
process of sinogram and image reconstruction from DECT measurements is
analyzed. Analytic estimates for the sinogram and monochromatic image pixel
variances and the CNR as functions of tube potentials, fluence, and virtual
monochromatic image (VMI) energy are derived, and then used in a phantom
experiment as an objective function for optimizing the tube settings to
minimize the image noise and maximize the CNR. Results: A non-trivial example
that shows the existence of singular solutions to the inversion of
sinograms-to-DECT measurements map was presented. Additionally, the optimal VMI
energy for maximal CNR was determined. The optimal energy VMI was found to be
the least noisy monochromatic image synthesized from the iodine and water
density images, and it was shown that using more general weights in combining
the two images linearly does not improve image quality. When the x-ray beam
filter material was fixed at 2mm of Aluminum and the photon fluence for low and
high kV scans were considered equal, the tube potential pair of 60/120 kV led
to the maximal CNR in the VMI formed at energy 55 KeV. Conclusions: Optimizing
DECT scan parameters to maximize the CNR can be done in a systematic way. Also
choosing the parameters that maximize the Jacobian determinant over the
sinogram domain would lead to more stable reconstructions due to the reduced
amplification of the measurement noise. Since the values of the Jacobian
determinant depend strongly on the imaging task, careful consideration of all
of the relevant factors is needed when implementing the proposed framework.
