Tingliang Zhuang

Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data

In this paper, a new image reconstruction scheme is presented based on Tuys cone-beam inversion scheme and its fan-beam counterpart. It is demonstrated that Tuys inversion scheme may be used to derive a new framework for fanbeam and cone-beam image reconstruction. In this new framework, images are reconstructed via filtering the backprojection image of differentiated projection data. The new framework is mathematically exact and is applicable to a general source trajectory provided the Tuy data sufficiency condition is satisfied. By choosing a piece-wise constant function for one of the components in the factorized weighting function, the filtering kernel is one dimensional, viz. the filtering process is along a straight line. Thus, the derived image reconstruction algorithm is mathematically exact and efficient. In the cone-beam case, the derived reconstruction algorithm is applicable to a large class of source trajectories where the pi-lines or the generalized pi-lines exist. In addition, the new reconstruction scheme survives the super-short scan mode in both the fan-beam and cone-beam cases provided the data are not transversely truncated. Numerical simulations were conducted to validate the new reconstruction scheme for the fan-beam case.

Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector

In this paper, we present a new algorithm designed for a specific data truncation problem in fan-beam CT. We consider a scanning configuration in which the fan-beam projection data are acquired from an asymmetrically positioned half-sized detector. Namely, the asymmetric detector only covers one half of the scanning field of view. Thus, the acquired fan-beam projection data are truncated at every view angle. If an explicit data rebinning process is not invoked, this data acquisition configuration will reek havoc on many known fan-beam image reconstruction schemes including the standard filtered backprojection (FBP) algorithm and the super-short-scan FBP reconstruction algorithms. However, we demonstrate that a recently developed fan-beam image reconstruction algorithm which reconstructs an image via filtering a backprojection image of differentiated projection data (FBPD) survives the above fan-beam data truncation problem. Namely, we may exactly reconstruct the whole image object using the truncated data acquired in a full scan mode (2pi angular range). We may also exactly reconstruct a small region of interest (ROI) using the truncated projection data acquired in a short-scan mode (less than 2pi angular range). The most important characteristic of the proposed reconstruction scheme is that an explicit data rebinning process is not introduced. Numerical simulations were conducted to validate the new reconstruction algorithm.

Development and evaluation of an exact fan-beam reconstruction algorithm using an equal weighting scheme via locally compensated filtered backprojection (LCFBP)

A novel exact fan-beam image reconstruction formula is presented and validated using both phantom data and clinical data. This algorithm takes the form of the standard ramp filtered backprojection (FBP) algorithm plus local compensation terms. This algorithm will be referred to as a locally compensated filtered backprojection (LCFBP). An equal weighting scheme is utilized in this algorithm in order to properly account for redundantly measured projection data. The algorithm has the desirable property of maintaining a mathematically exact result for: the full scan mode (2pi), the short scan mode (pi+ full fan angle), and the supershort scan mode [less than (pi+ full fan angle)]. Another desirable feature of this algorithm is that it is derivative-free. This feature is beneficial in preserving the spatial resolution of the reconstructed images. The third feature is that an equal weighting scheme has been utilized in the algorithm, thus the new algorithm has better noise properties than the standard filtered backprojection image reconstruction with a smooth weighting function. Both phantom data and clinical data were utilized to validate the algorithm and demonstrate the superior noise properties of the new algorithm.

A cone-beam FBP reconstruction algorithm for short-scan and super-short-scan source trajectories

Conventionally, the FDK algorithm is used to reconstruct images from cone-beam projections in many imaging systems. One advantage of this algorithm is its shift-invariant feature in the filtering process. In this paper, a new cone-beam reconstruction algorithm is derived for a single arc source trajectory. Examples of the arc trajectory include the full circular scan mode, a short-scan mode and a super-short-scan mode depending upon the angular range of the scanning path. Since the single arc does not satisfy Tuys data sufficiency condition, there is no mathematically exact algorithm. However, one advantage of this reconstruction is that the shift-invariance property has been preserved despite the lack of a mathematically complete data set. The new algorithm includes backprojections from three adjacent segments of the arc defined by T1(vector x), T2(vector x) and T3(vector x). Each backprojection step consists of a weighted combination of 1D Hilbert filtering of the modified cone-beam data along horizontal and non-horizontal directions. The non-horizontal filtering is a new feature of this FBP algorithm. For the full circle scanning path, this algorithm reduces to the conventional FDK algorithm plus a term involving a first order derivative filter. Numerical simulations have been performed to validate the algorithm.

C-arm based cone-beam CT using a two-concentric-arc source trajectory : system evaluation

The current x-ray source trajectory for C-arm based cone-beam CT is a single arc. Reconstruction from data acquired with this trajectory yields cone-beam artifacts for regions other than the central slice. In this work we present the preliminary evaluation of reconstruction from a source trajectory of two concentric arcs using a flat-panel detector equipped C-arm gantry (GE Healthcare Innova 4100 system, Waukesha, Wisconsin). The reconstruction method employed is a summation of FDK-type reconstructions from the two individual arcs. For the angle between arcs studied here, 30°, this method offers a significant reduction in the visibility of cone-beam artifacts, with the additional advantages of simplicity and ease of implementation due to the fact that it is a direct extension of the reconstruction method currently implemented on commercial systems. Reconstructed images from data acquired from the two arc trajectory are compared to those reconstructed from a single arc trajectory and evaluated in terms of spatial resolution, low contrast resolution, noise, and artifact level.

Helical cone-beam computed tomography image reconstruction algorithm for a tilted gantry with N-PI data acquisition

We present a cone-beam image reconstruction algorithm for helical CT scanning with a tilted gantry and N-PI data acquisition. When the gantry is tilted, the effective source trajectory in the patients reference frame lies on an elliptical cylinder, rather than on a circular cylinder as in the standard helical scanning mode. The aim of this work is to provide a means of reconstructing an image object directly from cone-beam projection data without transforming the image object into a virtual object and without rebinning projection data acquired for a real object into the projection data of the virtual object. This task has been accomplished by the application of an exact reconstruction algorithm, which utilizes an important geometrical property of the elliptical helical trajectory: the existence of generalized N-PI lines for a given image point. Based on this property, a mathematically exact image reconstruction scheme via filtering the backprojection image of differentiated projection data (FBPD) is applied to solve the reconstruction problem. Due to the gantry tilt, the required detector size is different from that of the standard helical trajectory (nontilted). A systematic analysis of the required detector size is presented. For an N-PI data acquisition scheme, an image may be reconstructed using data from an N-PI window, an (N?2)-PI window, and so on. Although the images reconstructed using an N-PI (N>1) window are noisier than the images reconstructed from a 1-PI window, a weighted-average scheme over reconstructed images is presented to generate a final image with significantly lower noise variance than that in the 1-PI data acquisition scheme. The image reconstruction algorithm was numerically validated using a mathematical phantom.

Exact fan-beam reconstruction via ramp-filtered backprojection and local compensation

A novel exact fan-beam image reconstruction formula is presented and validated using both mathematical phantom data and clinical data. This algorithm takes the form of the standard ramp filtered backprojection (FBP) algorithm plus local compensation terms. An equal weighting scheme is utilized in this algorithm in order to properly account for redundantly measured projection data. The algorithm has the desirable property of maintaining a mathematically exact result for: the full scan mode (2π), the short scan mode (π+ full fan angle), and the super-short scan mode (less than (π + full fan angle)). Another desirable feature of this algorithm is that it is derivative-free. The derivative-free nature of this algorithm distinguishes it from other exact fan-beam FBP algorithms.

TU‐D‐I‐611‐03: Cone‐Beam Image Reconstruction for Circular‐Arc Trajectories Via Shift‐Invariant Horizontal and Non‐Horizontal Filtering

Purpose: To propose and validate a novel shift‐invariant filtered backprojection (FBP) type cone‐beam reconstruction algorithm for circular‐arc scanning trajectories. This algorithm has been proposed to address two shortcomings in the FDK algorithm; namely, limited visibility of low contrast objects in the off‐center planes and the inability to provide clinically acceptable reconstruction when the scanning path is shorter than the short‐scan condition. Method and Materials: Based upon the application of an exact cone‐beam reconstruction algorithm to the case of a circular trajectory, which does not fulfill the Tuy data sufficiency condition, a new algorithm has been developed. The new algorithm differs from the heuristic FDK algorithm in that multiple sets of filtered data are utilized in reconstructing the value of a single image point. The new algorithm introduces non‐horizontal filtering which is not achievable by heuristic extension fan‐beam FBP reconstruction. In this manner more of the cone‐beam data is utilized in the filtering operation. The new algorithm also enables region‐of‐interest (ROI) reconstruction in a super‐short scan mode (less than the short‐scan angular range). Results:Computer simulations were performed using analytical data generated for a standard low contrast phantom. The new algorithm provided improved visualization of structures that lie in off‐center planes when compared with the FDK algorithm. In addition simulations were performed to validate the ROI reconstruction using a super‐short scan mode. Conclusion: The circular‐arc scanning trajectories are used frequently in cone‐beam CT on interventional C‐Arm systems, micro CT systems and cone‐beam CT guided radiation therapy. A new shift‐invariant FBP type cone‐beam reconstruction algorithm has been proposed and validated for this common source trajectory. In comparison with the standard FDK algorithm the new algorithm provides improved visualization of structures that lie in off‐center planes, and it enables a super‐short scan mode for ROI reconstruction.

TU‐EE‐A3‐02: Exact Fan‐Beam Image Reconstruction Algorithm for a Specific Truncation Problem: Asymmetrically Positioned Half‐Size Detector

Purpose: In nuclear medicine imaging, diagnostic x-ray CT imaging, and image guided radiation therapy truncation of the projection data may be present due to patient motion, inaccurate positioning or simply an insufficient detector. For fan-beam geometry, images reconstructed with truncated data suffer sever artifacts when reconstructed with the conventional filtered backprojection (FBP) algorithm. A new exact fan-beam image reconstruction algorithm is developed to solve a special case of the data truncation problem. In this configuration, fan-beam projection data are acquired using an asymmetric detector that covers only half of the field of view. Method and Materials: In order to solve this data truncation problem, the newly developed fan-beam image reconstruction algorithm via filtering the backprojection image of the differentiated projection data (FBPD) was employed. This algorithm enables line by line reconstruction in image space. The following observations about this FBPD algorithm are crucial to solve the data truncation problem: (1) for a given point in the backprojection image space, only one projection from each view angle is required to properly construct the backprojection image; (2) for each ray passing through a given image point from one source position, there is a conjugate ray passing through the same point. With truncated data, a 2π full scan is required to reconstruct the whole object, and a ROI reconstruction can be obtained using projection data from less than a 2π full scan. Results: Numerical simulations have been conducted using a Shepp-Logan phantom. Images reconstructed from the truncated data for scans of the entire object validate this reconstruction algorithm for the full 2π scan. In addition ROI reconstruction has been validated using projection data from less than a 2π full scan. Conclusion: This algorithm enables exact fan-beam image reconstruction from projection data acquired using an asymmetric detector which covers only half of the field of view.