**Publications**(47)

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_{a}(

**r**,

*E*)

*d*

**r**), of the object using a small number of energy-dependent bases, which plays an important role for estimating basis line-integrals in photon counting detector (PCD)-based computed tomography (CT). Recently, we found that low-order polynomials can model the smooth x-ray transmittance, i.e. object without contrast agents, with sufficient accuracy, and developed a computationally efficient three-step estimator. The algorithm estimates the polynomial coefficients in the first step, estimates the basis line-integrals in the second step, and corrects for bias in the third step. We showed that the three-step estimator was ~1,500 times faster than conventional maximum likelihood (ML) estimator while it provided comparable bias and noise. The three-step estimator was derived based on the modeling of x-ray transmittance; thus, the accurate modeling of x-ray transmittance is an important issue. For this purpose, we introduce a modeling of the x-ray transmittance via dictionary learning approach. We show that the relative modeling error of dictionary learning-based approach is smaller than that of the low-order polynomials.

^{6}counts per second per pixel has been obtained with a low output x-ray tube for CT operated between 0.01 mA and 6 mA at 140 keV and different source-to-detector distances. All detector noise counts are less that 20 keV which is sufficiently low for clinical CT. The energy resolution measured with the 60 keV photons from a

^{241}Am source is ~12%. In conclusion, our results demonstrate the potential for the application of the CdTe based photon counting detector to clinical CT systems. Our future plans include further performance improvement by incorporating drift structures to each detector pixel.

*J*energy bins. In this study, we investigate use of the data in these energy bins for material decomposition using an image domain approach. In this method, one image is reconstructed from projection data of each energy bin; thus, we have

*J*images from

*J*energy bins that are associated with attenuation coefficients with a narrow energy width. We assume that the spread of energies in each bin is small and thus that the attenuation can be modeled using an effective energy for each bin. This approximation allows us to linearize the problem, thus simplify the inversion procedure. We then fit

*J*attenuation coefficients at each location

**x**by the energy-attenuation function [5] and obtain either (1) photoelectric and Compton scattering components or (2) 2 or 3 basis-material components. We used computer simulations to evaluate this approach generating projection data with three types of acquisition schemes: (A) five monochromatic energies; (B) five energy bins with PCXD and an 80 kVp polychromatic x-ray spectrum; and (C) two kVp with an intensity integrating detector. Total attenuation coefficients of reconstructed images and calculated effective atomic numbers were compared with data published by National Institute of Standards and Technology (NIST). We developed a new materially defined "SmileyZ" phantom to evaluate the accuracy of the material decomposition methods. Preliminary results showed that material based 3-basis functions (bone, water and iodine) with PCXD with 5 energy bins was the most promising approach for material decomposition.

*f(t, r r)*. Here, we use one heart beat for each position

*r*so that the time information is retained. Next, the magnitude of the first derivative of

*f(t, r r)*with respect to time, i.e., |

*df/dt*|, is calculated and summed over a region-of-interest (ROI), which is called the mean-absolute difference (MAD). The initial estimation of the vector field are obtained using MAD for each ROI. Results of the preliminary study are presented.

^{(Psi})((Theta) ,(phi) ) and the first derivative of plane integral (3D Radon transform) p

^{(Psi})((Theta) ,(phi) ) are described using spherical harmonics with equi-angular sampling. Then, using Grangeat's formula, relationship between coefficients of spherical harmonics for g

^{(Psi})((Theta) ,(phi) ) and p

^{(Psi})((Theta) ,(phi) ) are found. Finally, a method has been developed to obtain p

^{(Psi})((Theta) ,(phi) ) from cone- beam projection data in which the object is partially scanned. Images are reconstructed using the 3D Radon backprojection with rebinning. Computer simulations were performed in order to verify this approach: Isolated (axially bounded) objects were scanned both with circular and helical orbits. Wen the orbit of the cone vertex does not satisfy Tuy's data sufficiency conditions, strong oblique shadows and blurring in the axial direction were shown in reconstructed coronal images. ON the other hand, if the trajectory satisfied Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction. In conclusion, a novel implementation of the Grangeat's algorithm for cone-beam image reconstruction using equi-angular sampling has been developed.

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