Yuchuan Wei

A general local reconstruction approach based on a truncated Hilbert transform

Exact image reconstruction from limited projection data has been a central topic in the computed tomography (CT) field. In this paper, we present a general region-of-interest/volume-of-interest (ROI/VOI) reconstruction approach using a truly truncated Hilbert transform on a line-segment inside a compactly supported object aided by partial knowledge on one or both neighboring intervals of that segment. Our approach and associated new data sufficient condition allows the most flexible ROI/VOI image reconstruction from the minimum account of data in both the fan-beam and cone-beam geometry. We also report primary numerical simulation results to demonstrate the correctness and merits of our finding. Our work has major theoretical potentials and innovative practical applications.

Data consistency based translational motion artifact reduction in fan-beam CT

A basic assumption in the classic computed tomography (CT) theory is that an object remains stationary in an entire scan. In biomedical CT/micro-CT, this assumption is often violated. To produce high-resolution images, such as for our recently proposed clinical micro-CT (CMCT) prototype, it is desirable to develop a precise motion estimation and image reconstruction scheme. In this paper, we first extend the Helgason-Ludwig consistency condition (HLCC) from parallel-beam to fan-beam geometry when an object is subject to a translation. Then, we propose a novel method to estimate the motion parameters only from sinograms based on the HLCC. To reconstruct the moving object, we formulate two generalized fan-beam reconstruction methods, which are in filtered backprojection and backprojection filtering formats, respectively. Furthermore, we present numerical simulation results to show that our approach is accurate and robust

Fractional scan algorithms for low-dose perfusion CT

One of the key considerations in CT perfusion is the X-ray dose received by the patient, since cine acquisition mode is typically used in which repeated x-ray exposure occurs at the same anatomical location. In this technical note, we propose a new approach for dose reduction in which the X-ray tube current is maintained and the number of projection views is reduced per gantry rotation. A projection interpolation algorithm and an image prediction algorithm are developed to address the incompleteness of such projection data. Both algorithms utilize a priori knowledge that the contrast-uptake in perfusion images is gradual and predictable. As a result, excellent perfusion images can be reconstructed at a fraction of the nominal radiation dose.

Lambda tomography with discontinuous scanning trajectories.

Lambda tomography (LT) is a well-known local reconstruction technology to reduce the radiation dose or accommodate a limited imaging geometry. After a theoretical analysis of the so-called Calderon operator (CO), the necessary conditions for exact LT reconstruction are presented in terms of the 2D and 3D COs. Based on our previous results on LT, a general scheme is proposed to construct exact LT formulae in terms of the 2D CO with multiple segment trajectories. Every 2D formula has a corresponding 3D cone-beam formula in the Feldkamp framework in terms of the 2D CO which was illustrated in a triple-segment case. Our simulation results verify the correctness and demonstrate the merits of the proposed scheme.

Integral Invariants for Computed Tomography

Using the group theory, we formulate integral invariants of projection data in fan-beam and cone-beam computed tomography (CT), which can be applied to sense an object motion and detect a contrast bolus arrival

Relation between the filtered backprojection algorithm and the backprojection algorithm in CT

In this letter, we present a new fan-beam CT formula, based on which we discuss the relation between the filtered backprojection (FBP) algorithm and the backprojection (BP) algorithm. Specifically, the FBP algorithm can be expressed in a series with its first-order approximation being the BP algorithm. As a result, we identify a link between X-ray CT and number theory.

General formulation for x-ray computed tomography

Over recent years, various exact cone-beam reconstruction algorithms have been proposed. The derivations of these algorithms are quite complicated, and often difficult to see the fundamental connections among these methods and their key steps. In this paper, we present a straightforward perspective based on the Fourier transform, which is a universal principle for parallel and divergent beam computed tomography (CT). The formulas in this paper are not only consistent with the latest findings in the field but also valid under more general conditions.

CT reconstruction filter design in the real space

Theoretically, the ramp filter for filter backprojection reconstruction in X-ray computed tomography (CT) is a generalized function, expressed as |ω| in the frequency domain and -1/(2π2t2) in the real space. The traditional method for designing a practical filter is to select a curve in the frequency domain which is close to the function |Οω| in some sense. Similarly, to design a practical filter one also can select a function in the real space which approximates the function -1/(2π2t2). Several approximations are studied, leading to either known or new filters. The image reconstructed using the new filter is comparable with that using the band-limited filter.

SU‐E‐J‐177: Improved Reconstruction Algorithm for Tomosynthesis Plus Few Discrete Projections

Purpose: Investigations over the past few years have demonstrated some of the benefits and shortfalls of tomosynthesis in radiation therapy for patient positioning or dose tracking. Tomosynthesis generates excellent image quality in one reconstruction plane; however, there is a loss of edge and frequency information in the additional planes due to the spatial incompleteness of the projection data. In this study, we investigate the results of a new discrete frequency interpolation technique (DFIT), which is used to incorporate tomosynthesis limited arc projection data and three additional “filling” projections. Methods: For the initial investigations, we simulated a Shepp‐Logan phantom with parallel beam geometry to generate 93 projections. 90 of these projections were over a tomosynthetic arc at one projection per degree. The remaining three projections were generated to fill in the next 90 degrees evenly (i.e. 22.5, 45, and 67.5 degrees from the end of the arc) to help “fill in” the incomplete data. Simple filtered backprojection (FBP) results show no improvement as FBP is designed for uniform distribution of projections. Per the projection slice theorem, the tomosynthesis data fills in a portion of the frequency plane. The remaining sparsely sampled area of the frequency plane is filled using linear interpolation from the end arc projections and the 3 discrete projections. The DFIT image is the sum of the FBP image and the inverse Fourier transform of the interpolated frequencies Results: The images by traditional FBP and DFIT are compared visually and using line profile plots. Additionally, contrast results are examined. The DFIT images show improved edge delineation in the usual tomosynthesis “blurred” direction and improves reconstructed contrast. Conclusions: The addition of limited “filling” discrete projections and DFIT can be used to improve the reconstruction accuracy and quality of short arc imaging. Research supported by Nucletron, B.V.

SU‐E‐J‐176: Further Investigation of Improved Reconstruction Algorithm for Tomosynthesis Plus Few Discrete Projections: Noisy Projections and TV Filtration

Purpose: Investigations over the past few years have demonstrated some of the benefits and shortfalls of tomosynthesis in radiation therapy for patient positioning or dose tracking. Tomosynthesis generates excellent image quality in one reconstruction plane; however, there is a loss of edge and frequency information in the additional planes due to the spatial incompleteness of the projection data. In our previous study, we demonstrated improved results from a new discrete frequency interpolation technique (DFIT), which is used to incorporate tomosynthesis limited arc projection data and three additional “filling” projections. Here, we continue investigation into DFIT by studying noisy projections for the data and incorporation of total variation (TV) noise reduction into the reconstruction processing. Methods: For this investigation, we simulated a Shepp‐Logan phantom to generate 93 parallel beam projections with ±5% uniform random noise. 90 of these projections were over a 90‐degree tomosynthetic arc. The remaining three projections were evenly spaced (i.e. 22.5, 45, and 67.5 degrees from the end of the arc) to help “fill in” the incomplete data. DFIT+TV was used to reconstructimages by interpolating frequency values into the gaps of the Fourier spectrum, inverse Fourier transforming from frequency to image space, adding the resultant image to a filtered backprojection (FBP) image, and finally applying a TV noise reduction step. Results: The images by traditional FBP, DFIT, FBP+TV and DFIT+TV are compared visually and using horizontal and vertical line profile plots. Additionally, contrast results are examined. The DFIT+TV images show improved edge delineation in the usual tomosynthesis “blurred” direction and improved reconstructed contrast. Conclusions: The addition of limited “filling” discrete projections and DFIT+TV can be used to improve the reconstruction accuracy and quality of short arc imaging. Future work will study DFIT+TV in the cone beam geometry. Research supported by Nucletron, B.V.