Page 1. 1162 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 53, NO. 3, JUNE 2006 Phantom Assessment o... more Page 1. 1162 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 53, NO. 3, JUNE 2006 Phantom Assessment of New Acquisition Geometries for Breast Pinhole SPECT Imaging Konstantin V. Bobkov, James E. Bowsher ...
The authors' research group has recently examined new types of collimator designs with the goal o... more The authors' research group has recently examined new types of collimator designs with the goal of improving sensitivity and lesion detection for head imaging. One of these collimator designs is a half-cone beam collimator. However, the sensitivity is reduced as objects are removed from the focal line and it does not satisfy Tuy's sufficiency condition. A potential solution to this problem is to use one parallel hole collimator in conjunction with two half-cone beam collimators on a triple camera single photon emission computed tomography (SPECT) system. The authors acquired projection data with a Defrise disk phantom filled with Tc-99m. A half-cone beam collimator with a focal length of 50 cm was placed on one head of a triple camera SPECT system. A low energy super high resolution (LESR) parallel hole collimator was placed on a second head. Different projection data sets were combined to model acquisition in the three headed gamma camera with three half-cone beam collimators, two half-cone beam and one parallel beam collimators and three parallel beam collimators. Image reconstruction used a modified maximum likelihood maximization-expectation (ML-EM) algorithm. For the reconstruction with three half-cone beam collimators, the authors observe axial blurring. This is eliminated with two half-cone beam and one parallel beam collimators. There is a lack of a sharp boundary along the axial direction of the three half-cone beam collimator configuration as opposed to other collimation configurations that had a well defined boundary
Journal of The American Mathematical Society, 2008
For X a compact Riemann surface of positive genus, the strange duality conjecture predicts that t... more For X a compact Riemann surface of positive genus, the strange duality conjecture predicts that the space of sections of certain theta bundle on moduli of bundles of rank r and level k is naturally dual to a similar space of sections of rank k and level r. We prove this conjecture for X generic in the moduli space of curves of a given genus.
We describe the attracting basins of the origin in &a... more We describe the attracting basins of the origin in &#179k+1 for the polynomial lifts of Lattès examples. We show that the boundary of these bounded pseudoconvex domains is a quotient of a compact spherical hypersurface, and we describe the singularities that appear. These domains are surprising, because they are very close to the ball, and admit non injective proper holomorphic
European Journal of Nuclear Medicine and Molecular Imaging, 2000
Pinhole single-photon emission tomography (SPET) has been proposed to improve the trade-off betwe... more Pinhole single-photon emission tomography (SPET) has been proposed to improve the trade-off between sensitivity and resolution for small organs located in close proximity to the pinhole aperture. This technique is hampered by artefacts in the non-central slices. These artefacts are caused by truncation and by the fact that the pinhole SPET data collected in a circular orbit do not contain sufficient information for exact reconstruction. The ordered subsets expectation maximization (OS-EM) algorithm is a potential solution to these problems. In this study a three-dimensional OS-EM algorithm was implemented for data acquired on a single-head gamma camera equipped with a pinhole collimator (PH OS-EM). The aim of this study was to compare the PH OS-EM algorithm with the filtered back-projection algorithm of Feldkamp, Davis and Kress (FDK)and with the conventional parallel-hole geometry as a whole,using a line source phantom, Picker’s thyroid phantom and a phantom mimicking the human cervical column. Correction for the angular dependency of the sensitivity in the pinhole geometrywas based on a uniform flood acquisition. The projection data were shifted according to the measured centre of rotation. No correction was made for attenuation, scatter or distance-dependent camera resolution. The resolution measured with the line source phantom showed a significant improvement with PH OS-EM as compared with FDK, especially in the axial direction. Using Picker’s thyroid phantom, one iteration with eight subsets was sufficient to obtain images with similar noise levels in uniform regions of interest to those obtained with the FDK algorithm. With these parameters the reconstruction time was 2.5 times longer than for the FDK method. Furthermore, there was a reduction in the artefacts caused by the circular orbit SPET acquisition. The images obtained from the phantom mimicking the human cervical column indicated that the improvement in image quality with PH OS-EM is relevant for future clinical useand that the improvements obtained using the OS-EM algorithm are more significant for the pinhole geometry than for the conventional parallel-hole geometry. We conclude that PH OS-EM is a practical and promising alternative for pinhole SPET reconstruction.
By means of suitable dual problems to the following global optimization problems: extremum{f(x): ... more By means of suitable dual problems to the following global optimization problems: extremum{f(x): x εM ⊂X}, wheref is a proper convex and lower-semicontinuous function andM a nonempty, arbitrary subset of a reflexive Banach spaceX, we derive necessary and sufficient optimality conditions for a global minimizer. The method is also applicable to other nonconvex problems and leads to at least necessary global optimality conditions.
Page 1. 1162 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 53, NO. 3, JUNE 2006 Phantom Assessment o... more Page 1. 1162 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 53, NO. 3, JUNE 2006 Phantom Assessment of New Acquisition Geometries for Breast Pinhole SPECT Imaging Konstantin V. Bobkov, James E. Bowsher ...
The authors' research group has recently examined new types of collimator designs with the goal o... more The authors' research group has recently examined new types of collimator designs with the goal of improving sensitivity and lesion detection for head imaging. One of these collimator designs is a half-cone beam collimator. However, the sensitivity is reduced as objects are removed from the focal line and it does not satisfy Tuy's sufficiency condition. A potential solution to this problem is to use one parallel hole collimator in conjunction with two half-cone beam collimators on a triple camera single photon emission computed tomography (SPECT) system. The authors acquired projection data with a Defrise disk phantom filled with Tc-99m. A half-cone beam collimator with a focal length of 50 cm was placed on one head of a triple camera SPECT system. A low energy super high resolution (LESR) parallel hole collimator was placed on a second head. Different projection data sets were combined to model acquisition in the three headed gamma camera with three half-cone beam collimators, two half-cone beam and one parallel beam collimators and three parallel beam collimators. Image reconstruction used a modified maximum likelihood maximization-expectation (ML-EM) algorithm. For the reconstruction with three half-cone beam collimators, the authors observe axial blurring. This is eliminated with two half-cone beam and one parallel beam collimators. There is a lack of a sharp boundary along the axial direction of the three half-cone beam collimator configuration as opposed to other collimation configurations that had a well defined boundary
Journal of The American Mathematical Society, 2008
For X a compact Riemann surface of positive genus, the strange duality conjecture predicts that t... more For X a compact Riemann surface of positive genus, the strange duality conjecture predicts that the space of sections of certain theta bundle on moduli of bundles of rank r and level k is naturally dual to a similar space of sections of rank k and level r. We prove this conjecture for X generic in the moduli space of curves of a given genus.
We describe the attracting basins of the origin in &a... more We describe the attracting basins of the origin in &#179k+1 for the polynomial lifts of Lattès examples. We show that the boundary of these bounded pseudoconvex domains is a quotient of a compact spherical hypersurface, and we describe the singularities that appear. These domains are surprising, because they are very close to the ball, and admit non injective proper holomorphic
European Journal of Nuclear Medicine and Molecular Imaging, 2000
Pinhole single-photon emission tomography (SPET) has been proposed to improve the trade-off betwe... more Pinhole single-photon emission tomography (SPET) has been proposed to improve the trade-off between sensitivity and resolution for small organs located in close proximity to the pinhole aperture. This technique is hampered by artefacts in the non-central slices. These artefacts are caused by truncation and by the fact that the pinhole SPET data collected in a circular orbit do not contain sufficient information for exact reconstruction. The ordered subsets expectation maximization (OS-EM) algorithm is a potential solution to these problems. In this study a three-dimensional OS-EM algorithm was implemented for data acquired on a single-head gamma camera equipped with a pinhole collimator (PH OS-EM). The aim of this study was to compare the PH OS-EM algorithm with the filtered back-projection algorithm of Feldkamp, Davis and Kress (FDK)and with the conventional parallel-hole geometry as a whole,using a line source phantom, Picker’s thyroid phantom and a phantom mimicking the human cervical column. Correction for the angular dependency of the sensitivity in the pinhole geometrywas based on a uniform flood acquisition. The projection data were shifted according to the measured centre of rotation. No correction was made for attenuation, scatter or distance-dependent camera resolution. The resolution measured with the line source phantom showed a significant improvement with PH OS-EM as compared with FDK, especially in the axial direction. Using Picker’s thyroid phantom, one iteration with eight subsets was sufficient to obtain images with similar noise levels in uniform regions of interest to those obtained with the FDK algorithm. With these parameters the reconstruction time was 2.5 times longer than for the FDK method. Furthermore, there was a reduction in the artefacts caused by the circular orbit SPET acquisition. The images obtained from the phantom mimicking the human cervical column indicated that the improvement in image quality with PH OS-EM is relevant for future clinical useand that the improvements obtained using the OS-EM algorithm are more significant for the pinhole geometry than for the conventional parallel-hole geometry. We conclude that PH OS-EM is a practical and promising alternative for pinhole SPET reconstruction.
By means of suitable dual problems to the following global optimization problems: extremum{f(x): ... more By means of suitable dual problems to the following global optimization problems: extremum{f(x): x εM ⊂X}, wheref is a proper convex and lower-semicontinuous function andM a nonempty, arbitrary subset of a reflexive Banach spaceX, we derive necessary and sufficient optimality conditions for a global minimizer. The method is also applicable to other nonconvex problems and leads to at least necessary global optimality conditions.
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