Gengsheng L. Zeng

Three-dimensional iterative reconstruction algorithms with attenuation and geometric point response correction

A three-dimensional iterative reconstruction algorithm which incorporates models of the geometric point response in the projector-backprojector is presented for parallel, fan, and cone beam geometries. The algorithms have been tested on an IBM 3090-600S supercomputer. The iterative EM reconstruction algorithm is 50 times longer with geometric response and photon attenuation models than without modeling these physical effects. An improvement in image quality in the reconstruction of projection data collected from a single-photon-emission computed tomography (SPECT) imaging system has been observed. Significant improvements in image quality are obtained when the geometric point response and attenuation are appropriately compensated. It is observed that resolution is significantly improved with attenuation correction alone. Using phantom experiments, it is observed that the modeling of the spatial system response imposes a smoothing without loss of resolution. >

Non-uniform attenuation correction using simultaneous transmission and emission converging tomography

Photon attenuation in cardiac single photon emission computed tomography (SPECT) is a major factor contributing to the quantitative inaccuracy and the decrease in sensitivity of lesion detection. A measured map of the attenuation distribution is used in combination with iterative reconstruction algorithms to accurately compensate for the variable attenuation in the chest. The transmission and emission data are acquired simultaneously using a multidetector, fan beam collimated SPECT system with a precisely aligned transmission line source (Tc-99m) at a different energy than the emission source (Tl-201). The contamination of transmission and emission data due to scatter and multiple photopeaks is removed based on measurements from the detectors acquiring only the emission data. The quantitative accuracy of cardiac SPECT is significantly improved using simultaneously acquired transmission and emission data which are obtained in clinically acceptable patient scanning times.<<ETX>>

Unmatched projector/backprojector pairs in an iterative reconstruction algorithm

Computational burden is a major concern when an iterative algorithm is used to reconstruct a three-dimensional (3-D) image with attenuation, detector response, and scatter corrections. Most of the computation time is spent executing the projector and backprojector of an iterative algorithm. Usually, the projector and the backprojector are transposed operators of each other. The projector should model the imaging geometry and physics as accurately as possible. Some researchers have used backprojectors that are computationally less expensive than the projectors to reduce computation time. This paper points out that valid backprojectors should satisfy a condition that the projector/backprojector matrix must not contain negative eigenvalues. This paper also investigates the effects when unmatched projector/backprojector pairs are used.

Three-dimensional SPECT reconstruction of combined cone-beam and fan-beam data

A SPECT system includes three gam camera heads (22a), (22b), (22c) which are mounted to a gantry (20) for rotation about a subject (12). The subject is injected with a source of emission radiation, which emission radiation is received by the camera heads. Camera head (22a) has a fan-beam collimator (24a) mounted on a radiation receiving face and generates fan-beam data indicative of the received emission radiation. The camera heads (22b) and (22c) each have a cone-beam collimator (24b), (24c) mounted respectively on their radiation receiving face and generate cone-beam data indicative of the received emission radiation. A transmission radiation source (26) is mounted opposite the camera head (22a) having the fan-beam collimator (24a). The fan-beam detector head (22a) further receives transmission radiation and generates fan-beam transmission radiation indicative thereof. A transmission data reconstruction processor (50) reconstructs the fan-beam transmission data. An emission data memory (110) separately stores the fan-beam and cone-beam emission data. Attenuation correction processors (78, 86) correct the emission data in accordance with the reconstructed attenuation data. An emission data reconstructor (72) reconstructs the corrected emission data into a corresponding three-dimensional image representation which is selectively displayed on a display (76) in a human-readable form.

Review of convergent beam tomography in single photon emission computed tomography

Investigation of convergent-beam single photon emission computed tomography (SPECT) is actively being pursued to evaluate its clinical potentials. Fan-beam, cone-beam, pin-hole and astigmatic collimators are being used with rotating gamma cameras having large crystal areas, to increase the sensitivity for emission and transmission computed tomography of small organs such as the thyroid, brain or heart. With new multi-detector SPECT systems, convergent-beam geometry offers the ability to simultaneously obtain emission and transmission data necessary to quantify uptake of radiopharmaceutical distributions in the heart. The development of convergent-beam geometry in SPECT requires the integration of hardware and software. In considering hardware, the optimum detector system for cone-beam tomography is a system that satisfies the data sufficiency condition for which the scanning trajectory intersects any plane passing through the reconstructed region of interest. However, the major development of algorithms has been for the data insufficient case of single planar orbit acquisitions. The development of these algorithms have made possible the preliminary evaluation of this technology and the imaging of brain and heart are showing significant potential for the clinical application of cone-beam tomography. Presently, significant research activity is pursuing the development of algorithms for data acquisitions that satisfy the data sufficiency condition and that can be implemented easily and inexpensively on clinical SPECT systems.

A cone-beam tomography algorithm for orthogonal circle-and-line orbit

A cone-beam algorithm which provides a practical implementation of B D Smiths cone-beam inversion formula is presented. For a cone-beam vertex orbit consisting of a circle and an orthogonal line. This geometry is easy to implement in a SPECT system, and it satisfies the cone-beam data sufficiency condition. The proposed algorithm is in the form of a convolution-back projection, and requires a pre-filtering procedure. Computer simulations show a reduction of the artifacts that are found with the Feldkamp algorithm where the cone-beam vertex orbit is a circle.

Total variation regulated EM algorithm

An iterative Bayesian reconstruction algorithm based on the total variation (TV) norm constraint is proposed. The motivation for using TV regularization is that it is extremely effective for recovering edges of images. The TV norm minimization, introduced in 1992 was shown to be effective for restoring blurred images with a Gaussian noise model and was demonstrated to be effective for noise suppression and edge preservation. The images were diffused according to a set of nonlinear anisotropic diffusion partial differential equations, which suffered from computational difficulties. This paper extends the TV norm minimization constraint to the field of SPECT image reconstruction with a Poisson noise model. The regularization norm is included in the ML-EM (maximum likelihood expectation maximization) algorithm. The partial differential equation approach is not utilized here. Reconstructions of computer simulations and patient data show that the proposed algorithm has the capacity to smooth the noise and maintain sharp edges without introducing over/under shoots and ripples around the edges.

Application of spherical harmonics to image reconstruction for the Compton camera

The Compton camera can collect SPECT data with high efficiency due to electronic collimation. The data acquired from a Compton camera are projections of source activity along cones and are approximated in this paper by cone-surface integrals. This paper proposes the use of an orthogonal spherical expansion to convert the cone-surface integrals into plane integrals. The conversion technique is efficient. Once the plane integrals are obtained, a 3D image can be reconstructed by the 3D Radon inversion formula. The algorithm is implemented and computer simulations are used to demonstrate the efficiency and accuracy of the proposed reconstruction algorithm.

Image reconstruction--a tutorial.

This paper is written for physicians and presents basic principles of image reconstruction in nuclear medicine. Both analytical and iterative methods are discussed without rigorous mathematics.

A study of reconstruction artifacts in cone beam tomography using filtered backprojection and iterative EM algorithms

Reconstruction artifacts in cone beam tomography are studied for filtered backprojection (Feldkamp) and iterative EM algorithms. The filtered backprojection algorithm uses a voxel-driven, interpolated backprojection to reconstruct the cone beam data, whereas the iterative EM algorithm performs ray-driven projection and backprojection operations for each iteration. Two weighting schemes for the projection and backprojection operations in the EM algorithm are studied. One weights each voxel by the length of the ray through the voxel and the other equates the value of a voxel to the functional value of the midpoint of the line intersecting the voxel, which is obtained by interpolating between eight neighboring voxels. Cone beam reconstruction artifacts such as rings, bright vertical extremities, and slice-to-slice cross-talk are not found with parallel beam and fan beam geometries. When using filtered backprojection and iterative EM algorithms, the line-length weighting is susceptible to ring artifacts which are improved by using interpolated projector-backprojectors. >