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Gengsheng L Zeng

Publications and source records attributed to Gengsheng L Zeng.

14 recordsLinked to original sources

An analytical algorithm for skew-slit collimator SPECT with uniform attenuation correction.

To replace the conventional pinhole (normal cone-beam) collimator, a novel skew-slit collimator was previously proposed and a Novikov-type algorithm developed to reconstruct images using the skew-slit geometry. The goal of this paper is to develop a reconstruction algorithm that has better noise control than the Novikov-type algorithm. The new algorithm is able to compensate for uniform attenuation, and computer simulation results show that reconstructed images are less noisy.

Algorithms↗

An immediate after-backprojection filtering method with blob-shaped window functions for voxel-based iterative reconstruction.

Spherically symmetric volume elements (blobs) have better resolution-noise performance than voxels because of the overlapping of their rotational symmetric basis functions; however, using blobs is more computationally expensive than using voxels due to blob overlap. In this paper, we propose an immediate after-backprojection filtering method (ABF) with blob-shaped window functions for a voxel-based reconstruction. We compared this method with the general voxel-based method (without filtering), the blob-based method, the voxel-based method with between-iteration filtering (BIF) and with post-filtering (POF), using computer simulations. Both the quality of the reconstruction and the computational cost were evaluated. The reconstruction quality was measured by the contrast recovery coefficient (CRC) versus the background noise. It is shown that images reconstructed using this method are characterized by less image noise and preserved image contrast in comparison with both the general voxel-based method and the voxel-based method with BIF. The improvement in image quality achieved by this method varies with the parameters chosen for the Kaiser-Bessel (KB) windows. As with blobs, wider KB windows achieve better contrast-noise trade-offs in the reconstructed images, but are more computationally expensive. When using a KB window of a = 2.0, alpha = 10.4 and m = 2, known as the basis function of a 'standard' blob, this new method achieves identical CRC-noise features to the blob-based method with 'standard' blobs. In addition, the ABF method can be combined with the post-filtering method to achieve better noise-resolution performance than the general voxel-based post-filtering method. The computational cost of the ABF method is slightly greater than that of the general voxel-based method, but much less than that of the blob-based method.

Algorithms↗

An analytical algorithm for skew-slit imaging geometry with nonuniform attenuation correction.

The pinhole collimator is currently the collimator of choice in small animal single photon emission computed tomography (SPECT) imaging because it can provide high spatial resolution and reasonable sensitivity when the animal is placed very close to the pinhole. It is well known that if the collimator rotates around the object (e.g., a small animal) in a circular orbit to form a cone-beam imaging geometry with a planar trajectory, the acquired data are not sufficient for an exact artifact-free image reconstruction. In this paper a novel skew-slit collimator is mounted instead of the pinhole collimator in order to significantly reduce the image artifacts caused by the geometry. The skew-slit imaging geometry is a more generalized version of the pinhole imaging geometry. The multiple pinhole geometry can also be extended to the multiple-skew-slit geometry. An analytical algorithm for image reconstruction based on the tilted fan-beam inversion is developed with nonuniform attenuation compensation. Numerical simulation shows that the axial artifacts are evidently suppressed in the skew-slit images compared to the pinhole images and the attenuation correction is effective.

Algorithms↗

An alternative proof of Bukhgeim and Kazantsev's inversion formula for attenuated fan-beam projections.

An inversion formula was developed by Bukhgeim and Kazantsev for attenuated fan-beam projections [Russian Academy of Science Siberian Branch: The Sobolev Institute of Mathematics (2002)]. The inversion formula was obtained by relating the attenuated fan-beam projections to unattenuated fan-beam projections and by trickily processing the unattenuated fan-beam projections. We show in this paper that the inversion formula can be readily obtained from Novikov's inversion formula for the two-dimensional (2D) attenuated radon transform. The derivation provides an alternative proof of Bukhgeim and Kazantsev's inversion formula by the use of transformation between parallel-beam coordinates and fan-beam coordinates and thus is quite elementary.

Algorithms↗

Convergence study of an accelerated ML-EM algorithm using bigger step size.

In SPECT/PET, the maximum-likelihood expectation-maximization (ML-EM) algorithm is getting more attention as the speed of computers increases. This is because it can incorporate various physical aspects into the reconstruction process leading to a more accurate reconstruction than other analytical methods such as filtered-backprojection algorithms. However, the convergence rate of the ML-EM algorithm is very slow. Several methods have been developed to speed it up, such as the ordered-subset expectation-maximization (OS-EM) algorithm. Even though OS-type algorithms can bring about significant acceleration in the iterative reconstruction, it is generally believed that ML-EM produces better images, in terms of statistical noise in the reconstruction. In this paper, we present an accelerated ML-EM algorithm with bigger step size and show its convergence characteristics in terms of variance noise and log-likelihood values. We also show some advantages of our method over other accelerating methods using additive forms.

Algorithms↗

Analytical fan-beam and cone-beam reconstruction algorithms with uniform attenuation correction for SPECT.

In this paper, we developed an analytical fan-beam reconstruction algorithm that compensates for uniform attenuation in SPECT. The new fan-beam algorithm is in the form of backprojection first, then filtering, and is mathematically exact. The algorithm is based on three components. The first one is the established generalized central-slice theorem, which relates the 1D Fourier transform of a set of arbitrary data and the 2D Fourier transform of the backprojected image. The second one is the fact that the backprojection of the fan-beam measurements is identical to the backprojection of the parallel measurements of the same object with the same attenuator. The third one is the stable analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan. The fan-beam algorithm is then extended into a cone-beam reconstruction algorithm, where the orbit of the focal point of the cone-beam imaging geometry is a circle. This orbit geometry does not satisfy Tuy's condition and the obtained cone-beam algorithm is an approximation. In the cone-beam algorithm, the cone-beam data are first backprojected into the 3D image volume; then a slice-by-slice filtering is performed. This slice-by-slice filtering procedure is identical to that of the fan-beam algorithm. Both the fan-beam and cone-beam algorithms are efficient, and computer simulations are presented. The new cone-beam algorithm is compared with Bronnikov's cone-beam algorithm, and it is shown to have better performance with noisy projections.

Algorithms↗

FBP Algorithms for Attenuated Fan-Beam Projections.

A filtered backprojection (FBP) reconstruction algorithm for attenuated fan-beam projections has been derived based on Novikov's inversion formula. The derivation uses a common transformation between parallel-beam and fan-beam coordinates. The filtering is shift-invariant. Numerical evaluation of the FBP algorithm is presented as well. As a special application, we also present a shift-invariant FBP algorithm for fan-beam SPECT reconstruction with uniform attenuation compensation. Several other fan-beam reconstruction algorithms are also discussed. In the attenuation-free case, our algorithm reduces to the conventional fan-beam FBP reconstruction algorithm.

Journal Article↗

A new simple iterative reconstruction algorithm for SPECT transmission measurement.

This paper proposes a new iterative reconstruction algorithm for transmission tomography and compares this algorithm with several other methods. The new algorithm is simple and resembles the emission ML-EM algorithm in form. Due to its simplicity, it is easy to implement and fast to compute a new update at each iteration. The algorithm also always guarantees non-negative solutions. Evaluations are performed using simulation studies and real phantom data. Comparisons with other algorithms such as convex, gradient, and logMLEM show that the proposed algorithm is as good as others and performs better in some cases.

Algorithms↗

Exact fan-beam and 4pi-acquisition cone-beam SPECT algorithms with uniform attenuation correction.

This paper presents analytical fan-beam and cone-beam reconstruction algorithms that compensate for uniform attenuation in single photon emission computed tomography. First, a fan-beam algorithm is developed by obtaining a relationship between the two-dimensional (2D) Fourier transform of parallel-beam projections and fan-beam projections. Using this relationship, 2D Fourier transforms of equivalent parallel-beam projection data are obtained from the fan-beam projection data. Then a quasioptimal analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan, is used to reconstruct the image. A cone-beam algorithm is developed by extending the fan-beam algorithm to 4pi solid angle geometry. The cone-beam algorithm is also an exact algorithm.

Algorithms↗

Cone-beam and fan-beam image reconstruction algorithms based on spherical and circular harmonics.

A cone-beam image reconstruction algorithm using spherical harmonic expansions is proposed. The reconstruction algorithm is in the form of a summation of inner products of two discrete arrays of spherical harmonic expansion coefficients at each cone-beam point of acquisition. This form is different from the common filtered backprojection algorithm and the direct Fourier reconstruction algorithm. There is no re-sampling of the data, and spherical harmonic expansions are used instead of Fourier expansions. As a special case, a new fan-beam image reconstruction algorithm is also derived in terms of a circular harmonic expansion. Computer simulation results for both cone-beam and fan-beam algorithms are presented for circular planar orbit acquisitions. The algorithms give accurate reconstructions; however, the implementation of the cone-beam reconstruction algorithm is computationally intensive. A relatively efficient algorithm is proposed for reconstructing the central slice of the image when a circular scanning orbit is used.

Algorithms↗

Nonuniform noise propagation by using the ramp filter in fan-beam computed tomography.

It is observed that when the homogeneity property of the ramp filter is used to derive a filtered backprojection algorithm in fan-beam tomography, the reconstructed images have nonstationary frequency components and nonstationary noise. When a short focal-length is used, higher frequency components are amplified more at the edge of the image than at the center of the image, resulting in higher noise at the edge of the image.

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Image reconstruction algorithm for a spinning strip CZT SPECT camera with a parallel slat collimator and small pixels.

This paper discusses the use of small pixels in a spinning CdZnTe single photon emission computed tomography (SPECT) camera that is mounted with a parallel slat collimator. In a conventional slat collimation configuration, there is a detector pixel between two adjacent collimator slats. In our design, the pixel size is halved. That is, there are two smaller pixels to replace a regular pixel between two adjacent slats while the collimator remains unchanged. It has an advantage over our older design that uses tilted slats. In order to acquire a complete data set the tilted-slat collimator must spin 360 degrees at each SPECT view while the proposed design requires only 180 degrees at each SPECT view. Computer simulations and phantom experiments have been carried out to investigate the performance of the small-pixel configuration. It is observed that this design has the potential to increase the spatial resolution of the detector while keeping photon counts the same.

Algorithms↗

Diffusion tensor MR imaging of principal directions: a tensor tomography approach.

A novel approach to reconstructing the principal directions of a diffusion tensor field directly from magnetic resonance imaging (MRI) data using a tensor tomography data acquisition approach was developed. If tensor eigenvalues are assumed to be known, the reconstruction of principal directions requires fewer measurements than the reconstruction of the full tensor field. The tensor tomography data acquisition method (rotating diffusion gradients) leads to a unique reconstruction of principal directions, whereas the conventional MRI acquisition technique (stationary diffusion gradients) leads to an ambiguous reconstruction of principal directions when the same number of measurements are used. A computer-generated phantom was used to simulate the diffusion tensor field in the mid-ventricular region of the myocardium. The principal directions of the diffusion tensor field were assumed to align with the fibre structure of the myocardium. An iterative algorithm was used to reconstruct the principal directions. Computer simulations verify that the proposed method provides accurate reconstruction of the principal directions of a diffusion tensor field.

Algorithms↗

Image reconstruction algorithm for a rotating slat collimator.

A slat collimator in single photon emission computed tomography consists of a set of parallel slats. As the collimator spins, the detector measures a one-dimensional projection data set. A complete data set can be obtained by rotating the detector/collimator assembly around the object (patient) while the collimator spins continuously. The measured projection data are assumed to be weighted planar integrals of the object. This paper describes the development of an approximate three-dimensional image reconstruction algorithm for a rotating/spinning slat collimator. This algorithm is in filtered backprojection form. Computer simulations were performed to verify the effectiveness of the algorithm.

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