A diagram of the proposed technique.
The material decomposition can be represented as a linear transformation from attenuation space (b) and (e) to material space (c) and (f). The attenuation coefficients for water and iodine are represented by vectors, and the axes of the ellipses around the vectors are the standard deviations of these measurements in a typical scan with our micro-CT system (b), (e). These correspond to the vectors and ellipses representing the relative concentrations (0–1) of water and iodine (c) and (f). When the energy settings are suboptimal (a), the vectors corresponding to water and iodine are close together (b), and the transformation amplifies the noise (c). When a better set of energy settings are chosen (d), the water and iodine vectors are farther apart (e), and the noise amplification is less pronounced (f). The condition number of the decomposition matrix corresponding to the improved settings is less than half of the condition number for the original settings.
The condition number of the material decomposition matrix as a function of voltage, without (a) and with (b) filters. The darkest region in B, 40 kVp with the tin filter and 55 kVp with the tungsten filter, indicated with the crosshairs, corresponds to the lowest condition number.
The spectral sensitivity of our system with the two x-ray energy settings. These functions include the contributions from the tube, filters, and detector.
Spectral basis functions.
Typical temporal basis functions and sensitivity function.
Examples of spectral-temporal sensitivity functions (a) and basis functions (b). These functions are normalized and dimensionless.
Reconstructed attenuation images from the simulated scan using both original projections and interpolated projections, without and with bilateral filtration. Images with the low energy setting at two cardiac phases are shown.
Measures of reconstruction quality at each iteration of the refinement process, starting with the result from the material decomposition (iteration 0): The RMSE of the estimated iodine concentration at all points in the iodine volumes at all points in time (a), the STD (b) and MTF (c) measured around the vial containing water, and the SE of the left ventricle (d).
Images of the water and iodine components at one cardiac phase, before and after iterative refinement.
Reconstructed images from the in vivo scan. An attenuation image reconstructed with all the projections is shown at the top. The material components at two cardiac phases are shown below, with water in grayscale and iodine in red.
A closer view of a coronal section of the iodine in the heart over eight phases of the cardiac cycle, with the same color map as in Fig. 11.
The volume of the left ventricle of the heart over eight phases of the cardiac cycle, calculated from segmented images.
Measurements of the reconstructed attenuation images from the simulation, with sorted projections and interpolated projections, without and with bilinear filtration.
Computation time of the steps of the reconstruction process for the in vivo study.
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