Biomedical subjects

Guang-Hong Chen

Publications and source records attributed to Guang-Hong Chen.

8 recordsLinked to original sources

PubMed2006

A shift-invariant filtered backprojection (FBP) cone-beam reconstruction algorithm for the source trajectory of two concentric circles using an equal weighting scheme.

In this paper, a shift-invariant filtered backprojection cone-beam image reconstruction algorithm is derived, based upon Katsevich's general inversion scheme, and validated for the source trajectory of two concentric circles. The source trajectory is complete according to Tuy's data sufficiency condition and is used as the basis for an exact image reconstruction algorithm. The algorithm proceeds according to the following steps. First, differentiate the cone-beam projection data with respect to the detector coordinates and with respect to the source trajectory parameter. The data are then separately filtered along three different orientations in the detector plane with a shift-invariant Hilbert kernel. Eight different filtration groups are obtained via linear combinations of weighted filtered data. Voxel-based backprojection is then carried out from eight sets of view angles, where separate filtered data are backprojected from each set according to the backprojection sets' associated filtration group. The algorithm is first derived for a scanning configuration consisting of two concentric and orthogonal circles. By performing an affine transformation on the image object, the developed image reconstruction algorithm has been generalized to the case where the two concentric circles are not orthogonal. Numerical simulations are presented to validate the reconstruction algorithm and demonstrate the dose advantage of the equal weighting scheme.

Algorithms↗

PubMed2006

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.

Algorithms↗

PubMed2005

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.

Algorithms↗

PubMed2005

A new data consistency condition for fan-beam projection data.

The sum of all attenuation data acquired in one view of parallel-beam projections is a view angle independent constant. This fact is known as a data consistency condition on the two-dimensional Radon transforms. It plays an important role in tomographic image reconstruction and artifact correction. In this paper, a novel fan-beam data consistency condition (FDCC) is derived and presented. Using the FDCC, individual projection data in one view of fan-beam projections can be estimated from filtering all other projection data measured from different view angles. Numerical simulations are performed to validate the new FDCC in correcting ring artifacts caused by malfunctioning detector cells.

Artifacts↗

PubMed2005

A novel extension of the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections.

The general goal of this paper is to extend the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections without rebinning the divergent fan-beam and cone-beam projections into parallel-beam projections directly. The basic idea is to establish a novel link between the local Fourier transform of the projection data and the Fourier transform of the image object. Analogous to the two- and three-dimensional parallel-beam cases, the measured projection data are backprojected along the projection direction and then a local Fourier transform is taken for the backprojected data array. However, due to the loss of the shift invariance of the image object in a single view of the divergent-beam projections, the measured projection data is weighted by a distance dependent weight w(r) before the local Fourier transform is performed. The variable r in the weighting function w(r) is the distance from the backprojected point to the x-ray source position. It is shown that a special choice of the weighting function, w(r)=1/r, will facilitate the calculations and a simple relation can be established between the Fourier transform of the image function and the local Fourier transform of the 1/r-weighted backprojection data array. Unlike the parallel-beam cases, a one-to-one correspondence does not exist for a local Fourier transform of the backprojected data array and a single line in the two-dimensional (2D) case or a single slice in the 3D case of the Fourier transform of the image function. However, the Fourier space of the image object can be built up after the local Fourier transforms of the 1/r-weighted backprojection data arrays are shifted and then summed in a laboratory frame. Thus the established relations Eq. (27) and Eq. (29) between the Fourier space of the image object and the Fourier transforms of the backprojected data arrays can be viewed as a generalized projection-slice theorem for divergent fan-beam and cone-beam projections. Once the Fourier space of the image function is built up, an inverse Fourier transform could be performed to reconstruct tomographic images from the divergent beam projections. Due to the linearity of the Fourier transform, an image reconstruction step can be performed either when the complete Fourier space is available or in parallel with the building of the Fourier space. Numerical simulations are performed to verify the generalized projection-slice theorem by using a disc phantom in the fan-beam case.

Algorithms↗

PubMed2004

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 Tuy's cone-beam inversion scheme and its fan-beam counterpart. It is demonstrated that Tuy's 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.

Algorithms↗

PubMed2003

A new framework of image reconstruction from fan beam projections.

In this paper, we present a unified framework to reconstruct images for both fan beam and cone beam projections. The important feature of our theoretical framework is that it does not depend on the classical concept of the Radon transform at all. This property allows us to directly generalize the ideas and techniques developed in this paper to the cone beam reconstruction problem. In this paper, we extract such a framework from developing a new image reconstruction scheme from fan beam projections. Our new scheme also provides us new understanding of fan beam reconstruction problem. Our main results for the fan beam reconstruction are the following: First, we derive a general reconstruction scheme, in which the data sufficiency condition is transparently revealed by the reconstruction formula. Specifically, the data sufficiency condition for an accurate reconstruction of a region of interest (ROI) is that all the lines passing through the ROI must intersect the source trajectory at least once. Second, we further simplify the general reconstruction scheme by following three major steps of our new framework: (i) using symmetries of intermediate function; (ii) handling the data redundancy; (iii) changing discrete summation over the possible focal points into an integral along the source trajectory. After these steps, we obtain a new filtered backprojection algorithm. The key characteristic of this new algorithm is to take derivative of measured data with respect to the trajectory parameter. In practice, we can trade this derivative to some other continuous functions. In the configuration of a circular source trajectory with a third generation arc/collinear detector, we demonstrate how to remove the undesirable derivative of measured projection data. It results in a new algorithm for the sequential reconstruction of a ROI with a general normalized weighting function.

Algorithms↗

PubMed2003

An alternative derivation of Katsevich's cone-beam reconstruction formula.

In this paper an alternative derivation of Katsevich's cone-beam image reconstruction algorithm is presented. The starting point is the classical Tuy's inversion formula. After (i) using the hidden symmetries of the intermediate functions, (ii) handling the redundant data by weighting them, (iii) changing the weighted average into an integral over the source trajectory parameter, and (iv) imposing an additional constraint on the weighting function, a filtered backprojection reconstruction formula from cone beam projections is derived. The following features are emphasized in the present paper: First, the nontangential condition in Tuy's original data sufficiency conditions has been relaxed. Second, a practical regularization scheme to handle the singularity is proposed. Third, the derivation in the cone beam case is in the same fashion as that in the fan-beam case. Our final cone-beam reconstruction formula is the same as the one discovered by Katsevich in his most recent paper. However, the data sufficiency conditions and the regularization scheme of singularities are different. A detailed comparison between these two methods is presented.

Algorithms↗