Shiying Zhao

A general exact reconstruction for cone-beam CT via backprojection-filtration

In this paper, we prove a generalized backprojection-filtration formula for exact cone-beam image reconstruction with an arbitrary scanning locus. Our proof is independent of the shape of the scanning locus, as long as the object is contained in a region where there is a chord through any interior point. As special cases, this generalized formula can be applied with cone-beam scanning along nonstandard spiral and saddle curves, as well as in an n-PI window setting. The algorithmic implementation and numerical results are described to support the correctness of our general claim.

A unified framework for exact cone‐beam reconstruction formulas

In this paper, we present concise proofs of several recently developed exact cone-beam reconstruction methods in the Tuy inversion framework, including both filtered-backprojection and backprojection-filtration formulas in the cases of standard spiral, nonstandard spiral, and more general scanning loci. While a similar proof of the Katsevich formula was previously reported, we present a new proof of the Zou and Pan backprojection-filtration formula. Our proof combines both odd and even data extensions so that only the cone-beam transform itself is utilized in the backprojection-filtration inversion. More importantly, our formulation is valid for general smooth scanning curves, in agreement with an earlier paper from our group [Ye, Zhao, Yu, and Wang, Proc. SPIE 5535, 293-300 (Aug. 6 2004)]. As a consequence of that proof, we obtain a new inversion formula, which is in a two-dimensional filtering backprojection format. A possibility for generalization of the Katsevich filtered-backprojection reconstruction method is also discussed from the viewpoint of this framework.

Ultra-low dose lung CT perfusion regularized by a previous scan.

RATIONALE AND OBJECTIVES A previous scan-regularized reconstruction (PSRR) method was proposed to reduce radiation dose and applied to lung perfusion studies. Normal and ultra-low-dose lung computed tomographic perfusion studies were compared in terms of the estimation accuracy of pulmonary functional parameters. MATERIALS AND METHODS A sequence of sheep lung scans were performed in three prone, anesthetized sheep at normal and ultra-low doses. A scan protocol was developed for the ultra-low-dose studies with electrocardiographic gating: time point 1 for a normal x-ray dose scan (100 kV, 150 mAs) and time points 2 to 21 for low-dose scans (80 kV, 17 mAs). A nonlinear diffusion-based post-filtering method was applied to the difference images between the low-dose images and the high-quality reference image. The final images at 20 time points were generated by fusing the reference image with the filtered difference images. RESULTS The power spectra of perfusion images and coherences in the normal scans showed a great improvement in image quality of the ultra-low-dose scans with PSRR relative to those without RSRR. The gamma variate fitting and the repeatability of the measurements of the mean transit time demonstrated that the key parameters of lung functions can be reliably accessed using PSRR. The variability of the ultra-low-dose scan results obtained using PSRR was not substantially different from that between two normal-dose scans. CONCLUSIONS This study demonstrates that an approximate 90% reduction in radiation dose is achievable using PSRR without compromising quantitative computed tomographic measurements of regional lung function.

A knowledge‐based cone‐beam x‐ray CT algorithm for dynamic volumetric cardiac imaging

With the introduction of spiral/helical multislice CT, medical x-ray CT began a transition into cone-beam geometry. The higher speed, thinner slice, and wider coverage with multislice/cone-beam CT indicate a great potential for dynamic volumetric imaging, with cardiac CT studies being the primary example. Existing ECG-gated cardiac CT algorithms have achieved encouraging results, but they do not utilize any time-varying anatomical information of the heart, and need major improvements to meet critical clinical needs. In this paper, we develop a knowledge-based spiral/helical multislice/cone-beam CT approach for dynamic volumetric cardiac imaging. This approach assumes the relationship between the cardiac status and the ECG signal, such as the volume of the left ventricle as a function of the cardiac phase. Our knowledge-based cardiac CT algorithm is evaluated in numerical simulation and patient studies. In the patient studies, the cardiac status is estimated initially from ECG data and subsequently refined with reconstructed images. Our results demonstrate significant image quality improvements in cardiac CT studies, giving clearly better clarity of the chamber boundaries and vascular structures. In conclusion, this approach seems promising for practical cardiac CT screening and diagnosis.

A backprojection-filtration algorithm for nonstandard spiral cone-beam CT with an n-PI-window

For applications in bolus-chasing computed tomography (CT) angiography and electron-beam micro-CT, the backprojection-filtration (BPF) formula developed by Zou and Pan was recently generalized by Ye et al to reconstruct images from cone-beam data collected along a rather flexible scanning locus, including a nonstandard spiral. A major implication of the generalized BPF formula is that it can be applied for n-PI-window-based reconstruction in the nonstandard spiral scanning case. In this paper, we design an n-PI-window-based BPF algorithm, and report the numerical simulation results with the 3D Shepp-Logan phantom and Defrise disk phantom. The proposed BPF algorithm consists of three steps: cone-beam data differentiation, weighted backprojection and inverse Hilbert filtration. Our simulated results demonstrate the feasibility and merits of the proposed algorithm.

Exact BPF and FBP algorithms for nonstandard saddle curves

A hot topic in cone-beam CT research is exact cone-beam reconstruction from a general scanning trajectory. Particularly, a nonstandard saddle curve attracts attention, as this construct allows the continuous periodic scanning of a volume-of-interest (VOI). Here we evaluate two algorithms for reconstruction from data collected along a nonstandard saddle curve, which are in the filtered backprojection (FBP) and backprojection filtration (BPF) formats, respectively. Both the algorithms are implemented in a chord-based coordinate system. Then, a rebinning procedure is utilized to transform the reconstructed results into the natural coordinate system. The simulation results demonstrate that the FBP algorithm produces better image quality than the BPF algorithm, while both the algorithms exhibit similar noise characteristics.

Exact reconstruction for cone-beam scanning along nonstandard spirals and other curves

In this article we consider cone-beam CT projections along a nonstandard 3-D spiral with variable radius and variable pitch. Specifically, we generalize an exact image reconstruction formula by Zou and Pan (2004a) and (2004b) to the case of nonstandard spirals, by giving a new, analytic proof of the reconstruction formula. Our proof is independent of the shape of the spiral, as long as the object is contained in a region inside the spiral, where there is a PI line passing through any interior point. Our generalized reconstruction formula can also be applied to much more general situations, including cone-beam scanning along standard (Pack, et al. 2004) and nonstandard saddle curves, and any smooth curve from one endpoint of a line segment to the other endpoint, for image reconstruction of that line segment. In other words, our results can be regarded as a generalization of Orlovs classical papers (1975) to cone-beam scanning.

Wavelet sampling and localization schemes for the Radon transform in two dimensions

Two theorems are presented for wavelet decompositions of the two-dimensional Radon transform. The rst theorem establishes an upper error bound in L 2 -norm between the Radon transform and its wavelet approximation whose coecients at dierent scales are estimated from Radon data acquired at corresponding sampling rates. The second theorem gives an estimate of the accuracy of a local image reconstructed from localized Radon data at multiple levels. These results show how to design a multilevel sampling and localization strategy for parallel-beam scanning by using wavelet regularity and vanishing moment characteristics, clarify the interaction between the wavelet structure and the essential bandwidth of an object image, and provide guidelines for wavelet local tomography.

Local ROI Reconstruction via Generalized FBP and BPF Algorithms along More Flexible Curves

We study the local region-of-interest (ROI) reconstruction problem, also referred to as the local CT problem. Our scheme includes two steps: (a) the local truncated normal-dose projections are extended to global dataset by combining a few global low-dose projections; (b) the ROI are reconstructed by either the generalized filtered backprojection (FBP) or backprojection-filtration (BPF) algorithms. The simulation results show that both the FBP and BPF algorithms can reconstruct satisfactory results with image quality in the ROI comparable to that of the corresponding global CT reconstruction.

A Parallel Implementation of the Katsevich Algorithm for 3-D CT Image Reconstruction

Yu and Wang [1, 2] implemented the first theoretically exact spiral cone-beam reconstruction algorithm developed by Katsevich [3, 4]. This algorithm requires a high computational cost when the data amount becomes large. Here we study a parallel computing scheme for the Katsevich algorithm to facilitate the image reconstruction. Based on the proposed parallel algorithm, several numerical tests are conducted on a high performance computing (HPC) cluster with thirty two 64-bit AMD-based Opteron processors. The standard phantom data [5] is used to establish the performance benchmarks. The results show that our parallel algorithm significantly reduces the reconstruction time, achieving high speedup and efficiency.