Convolutional image reconstruction for quantitative single photon emission computed tomography

Two image reconstruction algorithms have been investigated. They are based on filtered backprojection, and are useful when the tissue attenuation is considered to be uniform in the object. The first method uses a weighted backprojection, the weighting factor being determined in such a way that the photon attenuation is compensated with low noise propagation. The parameters involved in the convolution kernel and the correction function were determined by a computer iteration program. The second method, which is a simplified version of the first, uses conventional backprojection, and takes a shorter computation time than the first method. The statistical noise of an image can be minimised by suitable positioning of the coordinate origin for the reconstruction. The theory of the two methods, their performance on statistical noise and some results of mathematical and experimental phantom studies are described.     

Exact filtered backprojection reconstruction for dynamic pitch helical cone beam computed tomography

We present an exact filtered backprojection reconstruction formula for helical cone beam computed tomography in which the pitch of the helix varies with time. We prove that the resulting algorithm, which is functionally identical to the constant pitch case, provides exact reconstruction provided that the projection of the helix onto the detector forms convex boundaries and that PI lines are unique. Furthermore, we demonstrate that both of these conditions are satisfied provided the sum of the translational velocity and the derivative of the translational acceleration does not change sign. As a special case, we show that gantry tilt can also be handled by our dynamic pitch formula. Simulation results demonstrate the resulting algorithm.     

A local region of interest image reconstruction via filtered backprojection for fan-beam differential phase-contrast computed tomography

Recently, x-ray differential phase contrast computed tomography (DPC-CT) has been experimentally implemented using a conventional source combined with several gratings. Images were reconstructed using a parallel-beam reconstruction formula. However, parallel-beam reconstruction formulae are not directly applicable for a large image object where the parallel-beam approximation fails. In this note, we present a new image reconstruction formula for fan-beam DPC-CT. There are two major features in this algorithm: (1) it enables the reconstruction of a local region of interest (ROI) using data acquired from an angular interval shorter than 180 degrees + fan angle and (2) it still preserves the filtered backprojection structure. Numerical simulations have been conducted to validate the image reconstruction algorithm.     

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 pointwise limit theorem for filtered backprojection in computed tomography

Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in the norm sense. In this paper, we use the method of limited bandwidth to handle filtered backprojection-based image reconstruction when the spectrum of an underlying image is not absolutely integrable. Our main contribution is, assuming the method of limited bandwidth, to prove a pointwise limit theorem for a class of functions practically relevant and quite general. Further work is underway to extend the theory and explore its practical applications.     

A filtered backprojection algorithm for cone beam reconstruction using rotational filtering under helical source trajectory

With the evolution from multi-detector-row CT to cone beam (CB) volumetric CT, maintaining reconstruction accuracy becomes more challenging. To combat the severe artifacts caused by a large cone angle in CB volumetric CT, three-dimensional reconstruction algorithms have to be utilized. In practice, filtered backprojection (FBP) reconstruction algorithms are more desirable due to their computational structure and image generation efficiency. One of the CB-FBP reconstruction algorithms is the well-known FDK algorithm that was originally derived for a circular x-ray source trajectory by heuristically extending its two-dimensional (2-D) counterpart. Later on, a general CB-FBP reconstruction algorithm was derived for noncircular, such as helical, source trajectories. It has been recognized that a filtering operation in the projection data along the tangential direction of a helical x-ray source trajectory can significantly improve the reconstruction accuracy of helical CB volumetric CT. However, the tangential filtering encounters latitudinal data truncation, resulting in degraded noise characteristics or data manipulation inefficiency. A CB-FBP reconstruction algorithm using one-dimensional rotational filtering across detector rows (namely CB-RFBP) is proposed in this paper. Although the proposed CB-RFBP reconstruction algorithm is approximate, it approaches the reconstruction accuracy that can be achieved by exact helical CB-FBP reconstruction algorithms for moderate cone angles. Unlike most exact CB-FBP reconstruction algorithms in which the redundant data are usually discarded, the proposed CB-RFBP reconstruction algorithm make use of all available projection data, resulting in significantly improved noise characteristics and dose efficiency. Moreover, the rotational filtering across detector rows not only survives the so-called long object problem, but also avoids latitudinal data truncation existing in other helical CB-FBP reconstruction algorithm in which a tangential filtering is carried out, providing better noise characteristics, dose efficiency and data manipulation efficiency.     

Quantitative pulmonary single photon emission computed tomography for radiotherapy applications.

Pulmonary imaging using single photon emission computed tomography (SPECT) is the focus of current radiotherapy research, including dose-response analysis and three-dimensional (3D) radiation treatment planning. Improvement in the quantitative capability of SPECT may help establish its potential role in this application as well as others requiring accurate knowledge of pulmonary blood flow. The purposes of this study were to quantitatively evaluate SPECT filtered backprojection (FBP) and ordered subset-expectation maximization (OS-EM) reconstruction implementations for measuring absolute activity concentration in lung phantom experiments, and to incorporate quantitative SPECT techniques in 3D-RTP for lung cancer. Quantitative FBP (nonuniform iterative Chang attenuation compensation, scatter correction, and 3D postreconstruction Metz filtering) and OS-EM implementations were compared with a "clinical" implementation of FBP (uniform multiplicative Chang attenuation compensation and post-reconstruction von Hann filtering), for their ability to improve quantification of inactive and active spherical defects in the lungs of an anthropomorphic torso phantom. Activity concentration estimates were found to depend on many factors, such as region of interest size, scatter subtraction constant (k), postreconstruction deconvolution filtering and, in the case of OS-EM, total number of iterations. In general, reconstruction implementations incorporating compensation for nonuniform attenuation and scatter provided reduced bias relative to the clinical implementation. Potential applications to lung radiotherapy, including dose-functional histograms and treatment planning are also discussed. SPECT has the potential to provide accurate estimates of lung activity distributions that, together with improved image quality, may be useful for the study and prediction of therapeutic response.     

A three-dimensional-weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT-helical scanning

Based on the structure of the original helical FDK algorithm, a three-dimensional (3D)-weighted cone beam filtered backprojection (CB-FBP) algorithm is proposed for image reconstruction in volumetric CT under helical source trajectory. In addition to its dependence on view and fan angles, the 3D weighting utilizes the cone angle dependency of a ray to improve reconstruction accuracy. The 3D weighting is ray-dependent and the underlying mechanism is to give a favourable weight to the ray with the smaller cone angle out of a pair of conjugate rays but an unfavourable weight to the ray with the larger cone angle out of the conjugate ray pair. The proposed 3D-weighted helical CB-FBP reconstruction algorithm is implemented in the cone-parallel geometry that can improve noise uniformity and image generation speed significantly. Under the cone-parallel geometry, the filtering is naturally carried out along the tangential direction of the helical source trajectory. By exploring the 3D weighting's dependence on cone angle, the proposed helical 3D-weighted CB-FBP reconstruction algorithm can provide significantly improved reconstruction accuracy at moderate cone angle and high helical pitches. The 3D-weighted CB-FBP algorithm is experimentally evaluated by computer-simulated phantoms and phantoms scanned by a diagnostic volumetric CT system with a detector dimension of 64 x 0.625 mm over various helical pitches. The computer simulation study shows that the 3D weighting enables the proposed algorithm to reach reconstruction accuracy comparable to that of exact CB reconstruction algorithms, such as the Katsevich algorithm, under a moderate cone angle (4 degrees) and various helical pitches. Meanwhile, the experimental evaluation using the phantoms scanned by a volumetric CT system shows that the spatial resolution along the z-direction and noise characteristics of the proposed 3D-weighted helical CB-FBP reconstruction algorithm are maintained very well in comparison to the FDK-type algorithms. Moreover, the experimental evaluation by clinical data verifies that the proposed 3D-weighted CB-FBP algorithm for image reconstruction in volumetric CT under helical source trajectory meets the challenges posed by diagnostic applications of volumetric CT imaging.     

Rapid calculation of detectability in Bayesian single photon emission computed tomography

We consider the calculation of lesion detectability using a mathematical model observer, the channelized Hotelling observer (CHO), in a signal-known-exactly/background-known-exactly detection task for single photon emission computed tomography (SPECT). We focus on SPECT images reconstructed with Bayesian maximum a posteriori methods. While model observers are designed to replace time-consuming studies using human observers, the calculation of CHO detectability is usually accomplished using a large number of sample images, which is still time consuming. We develop theoretical expressions for a measure of detectability, the signal-to-noise-ratio (SNR) of a CHO observer, that can be very rapidly evaluated. Key to our expressions are approximations to the reconstructed image covariance. In these approximations, we use methods developed in the PET literature, but modify them to reflect the different nature of attenuation and distance-dependent blur in SPECT. We validate our expressions with Monte Carlo methods. We show that reasonably accurate estimates of the SNR can be obtained at a computational expense equivalent to approximately two projection operations, and that evaluating SNR for subsequent lesion locations requires negligible additional computation.     

Brain single photon emission computed tomography findings in depressive pseudodementia patients

BACKGROUND: Recently, there have been studies suggesting that depressive pseudodementia would include early-stage dementing disorder. Through the comparison of the 99mTc-HMPAO single photon emission computed tomography (SPECT) image of depressive pseudodementia subjects, healthy comparison subjects, depressed subjects free of cognitive impairment, and dementia of Alzheimer's type (DAT) subjects, we aimed to see part of pathophysiology of the depressive pseudodementia of elderly patients. METHODS: Study subjects consisted of seven patients with depressive pseudodementia, seven healthy comparison subjects, seven patients with depression free of cognitive impairment, and eleven patients with DAT. Depression patients were diagnosed according to DSM-III-R. DAT patients were diagnosed by DSM III-R and NINCDS-ADRDA criteria of DAT. Other measures for assessment include Hamilton Rating Scale for Depression and Mini Mental State Exam. All underwent 99mTc-HMPAO SPECT scan. The images of each group were analyzed using statistical parametric mapping of Friston, which compares the images on voxel-by-voxel basis. RESULTS: The results were as follows (1) The DAT group showed significant decreases of cerebral blood flow (CBF) in the right frontal, right temporal region, and both parietal regions as compared with control group (P < 0.05). (2) The depression group showed a significant decrease of CBF in the left frontal region as compared with control group (P < 0.05). (3) The depressive pseudodementia group showed significant decreases of CBF in both parietal regions as compared with control group (P < 0.05). (4) The depressive pseudodementia group showed significant decreases of CBF in the right temporal region and both parietal regions as compared with depression group (P < 0.05). (5) The DAT group showed significant decreases of CBF in the right temporal region, both frontal regions, and both parietal regions as compared with depressive pseudodementia group (P < 0.05). LIMITATIONS: The small number of subjects may make it difficult to generalize from our results. Because decreased CBF in depressive pseudodementia is found while the subjects were depressed, we cannot tell whether it is a state marker or a trait marker. CONCLUSIONS: The depressive pseudodementia group showed decreased CBF in the temporo-parietal region, similar to that of the DAT group and different from that of the depression group.     

A comparison of attenuation correction methods for quantitative single photon emission computed tomography

Transverse section tomograms of experimental phantoms and patients have been obtained using a GE 400T camera and a filtered back-projection reconstruction technique. These tomograms have been compared with the corresponding sections reconstructed from the same tomographic projection data, but using iterative algorithms with correction for photon attenuation. The comparison assesses the importance of including a correction for attenuation as well as demonstrating how closely a simple geometric attenuation correction, applied to the filtered back-projection reconstruction method, approximates to a more accurate correction incorporated in the computation of line integrals during iterative reconstruction. A comparison is also made between the behaviour of reconstruction algorithms with simulated projection data and real data in terms of convergence properties, and some shortcomings arising from simulation are noted.     

Area weighted convolutional interpolation for data reprojection in single photon emission computed tomography

A data reprojection algorithm has been developed for use in single photon emission computed tomography on an array processor equipped computer system. The algorithm makes use of an accurate representation of pixel activity (uniform square pixel model of intensity distribution), and is rapidly performed due to the efficient handling of an array-based algorithm and the fast Fourier transform on parallel processing hardware. The algorithm consists of using a pixel driven nearest-neighbor projection operation to an array of subdivided projection bins. The subdivided project bin array is then convolved with the angle-dependent projection of the area of a uniform square pixel and compressed to original bin size. The new algorithm has thus been named the area weighted convolution (AWC) method of interpolation. When compared to nearest-neighbor and linear interpolation algorithms, the new AWC algorithm was found to be more accurate, having an accuracy approaching that of the line length algorithm. It also yielded an easier and more efficient implementation on parallel hardware than line length or linear interpolation, with faster execution times than either.     

An electronically collimated gamma camera for single photon emission computed tomography. Part II: Image reconstruction and preliminary experimental measurements

Iterative algorithms have been investigated for reconstructing images from data acquired with a new type of gamma camera based upon an electronic method of collimating gamma radiation. The camera is composed of two detection systems which record a sequential interaction of the emitted gamma radiation. Coincident counting in accordance with Compton scattering kinematics leads to a localization of activity upon a multitude of conical surfaces throughout the object. A two-stage reconstruction procedure in which conical line projection images as seen by each position sensing element of the first detector are reconstructed in the first stage, and tomographic images are reconstructed in the second stage, has been developed. Computer simulation studies of both stages and first-stage reconstruction studies with preliminary experimental data are reported. Experimental data were obtained with one detection element of a prototype germanium detector. A microcomputer based circuit was developed to record coincident counts between the germanium detector and an uncollimated conventional scintillation camera. Point sources of Tc-99m and Cs-137 were used to perform preliminary measurements of sensitivity and point spread function characteristics of electronic collimation.     

Modifying constrained least-squares restoration for application to single photon emission computed tomography projection images

Image restoration methods have been shown to increase the contrast of nuclear medicine images by decreasing the effects of scatter and septal penetration. Image restoration can also reduce the high-frequency noise in the image. This study applies constrained least-squares (CLS) restoration to the projection images of single photon emission computed tomography (SPECT). In a previous study, it was noted that CLS restoration has the potential advantage of automatically adapting to the blurred object. This potential is confirmed using planar images. CLS restoration is then modified to improve its performance when applied to SPECT projection image sets. The modification was necessary because the Poisson noise in low count SPECT images causes considerable variation in the CLS filter. On phantom studies, count-dependent Metz restoration was slightly better than the modified CLS restoration method, according to measures of contrast and noise. However, CLS restoration was generally judged as yielding the best results when applied to clinical studies, apparently because of its ability to adapt to the image being restored.     

A cone beam filtered backprojection (CB-FBP) reconstruction algorithm for a circle-plus-two-arc orbit.

The circle-plus-arc orbit possesses advantages over other "circle-plus" orbits for the application of x-ray cone beam (CB) volume CT in image-guided interventional procedures requiring intraoperative imaging, in which movement of the patient table is to be avoided. A CB circle-plus-two-arc orbit satisfying the data sufficiency condition and a filtered backprojection (FBP) algorithm to reconstruct longitudinally unbounded objects is presented here. In the circle suborbit, the algorithm employs Feldkamp's formula and another FBP implementation. In the arc suborbits, an FBP solution is obtained originating from Grangeat's formula, and the reconstruction computation is significantly reduced using a window function to exclude redundancy in Radon domain. The performance of the algorithm has been thoroughly evaluated through computer-simulated phantoms and preliminarily evaluated through experimental data, revealing that the algorithm can regionally reconstruct longitudinally unbounded objects exactly and efficiently, is insensitive to the variation of the angle sampling interval along the arc suborbits, and is robust over practical x-ray quantum noise. The algorithm's merits include: only 1D filtering is implemented even in a 3D reconstruction, only separable 2D interpolation is required to accomplish the CB backprojection, and the algorithm structure is appropriate for parallel computation.     

Monte Carlo evaluation of Compton scatter subtraction in single photon emission computed tomography

In single photon emission computed tomography (SPECT), Compton scattering produces a background that degrades the image quality and contributes erroneously to quantitative measurements. A clinically implementable compensation algorithm has previously been reported that subtracts a Compton scatter image, acquired in an energy window set below the energy of the photopeak, from the primary image acquired in the photopeak window. We present an evaluation and justification of the assumptions made in the previous empirical development of the subtraction algorithm. A Monte Carlo model of the SPECT system in which the Compton scattered vents may be followed independently of the nonscattered events was used to evaluate this subtraction technique. Simulation shows that the assumptions made in the experimental application of this algorithm were valid. Specifically (1) the "scatter" energy window used in the experiment (91-125 keV for imaging Tc-99m) contains only scattered events, (2) the shape of the line spread function (LSF) for the events in the scatter window is a reasonable approximation to the shape of the scatter in the photopeak window, and (3) the ratio of the number of scattered events in the photopeak window to the number of events in the scatter window is 0.57, close to the value of 0.5 derived heuristically. Thus, Monte Carlo simulation validates the basic assumptions underlying the empirical implementation of the scatter subtraction algorithm.     

Iterative concurrent reconstruction algorithms for emission computed tomography

Direct reconstruction techniques, such as those based on filtered backprojection, are typically used for emission computed tomography (ECT), even though it has been argued that iterative reconstruction methods may produce better clinical images. The major disadvantage of iterative reconstruction algorithms, and a significant reason for their lack of clinical acceptance, is their computational burden. We outline a new class of 'concurrent' iterative reconstruction techniques for ECT in which the reconstruction process is reorganized such that a significant fraction of the computational processing occurs concurrently with the acquisition of ECT projection data. These new algorithms use the 10-30 min required for acquisition of a typical SPECT scan to iteratively process the available projection data, significantly reducing the requirements for post-acquisition processing. These algorithms are tested on SPECT projection data from a Hoffman brain phantom acquired with a 2 x 10(5) counts in 64 views each having 64 projections. The SPECT images are reconstructed as 64 x 64 tomograms, starting with six angular views. Other angular views are added to the reconstruction process sequentially, in a manner that reflects their availability for a typical acquisition protocol. The results suggest that if T s of concurrent processing are used, the reconstruction processing time required after completion of the data acquisition can be reduced by at least 1/3T s.     

A three-dimensional weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT under a circular source trajectory

The original FDK algorithm proposed for cone beam (CB) image reconstruction under a circular source trajectory has been extensively employed in medical and industrial imaging applications. With increasing cone angle, CB artefacts in images reconstructed by the original FDK algorithm deteriorate, since the circular trajectory does not satisfy the so-called data sufficiency condition (DSC). A few 'circular plus' trajectories have been proposed in the past to help the original FDK algorithm to reduce CB artefacts by meeting the DSC. However, the circular trajectory has distinct advantages over other scanning trajectories in practical CT imaging, such as head imaging, breast imaging, cardiac, vascular and perfusion applications. In addition to looking into the DSC, another insight into the CB artefacts existing in the original FDK algorithm is the inconsistency between conjugate rays that are 180 degrees apart in view angle (namely conjugate ray inconsistency). The conjugate ray inconsistency is pixel dependent, varying dramatically over pixels within the image plane to be reconstructed. However, the original FDK algorithm treats all conjugate rays equally, resulting in CB artefacts that can be avoided if appropriate weighting strategies are exercised. Along with an experimental evaluation and verification, a three-dimensional (3D) weighted axial cone beam filtered backprojection (CB-FBP) algorithm is proposed in this paper for image reconstruction in volumetric CT under a circular source trajectory. Without extra trajectories supplemental to the circular trajectory, the proposed algorithm applies 3D weighting on projection data before 3D backprojection to reduce conjugate ray inconsistency by suppressing the contribution from one of the conjugate rays with a larger cone angle. Furthermore, the 3D weighting is dependent on the distance between the reconstruction plane and the central plane determined by the circular trajectory. The proposed 3D weighted axial CB-FBP algorithm can be implemented in either the native CB geometry or the so-called cone-parallel geometry. By taking the cone-parallel geometry as an example, the experimental evaluation shows that, up to a moderate cone angle corresponding to a detector dimension of 64 x 0.625 mm, the CB artefacts can be substantially suppressed by the proposed algorithm, while advantages of the original FDK algorithm, such as the filtered backprojection algorithm structure, 1D ramp filtering and data manipulation efficiency, are maintained.     

Comparison of relative cerebral blood flow maps using pseudo-continuous arterial spin labeling and single photon emission computed tomography

Pseudo‐continuous arterial spin labeling (PCASL) MRI is a relatively new arterial spin labeling technique and has the potential to extend the cerebral blood flow (CBF) measurement to all tissue types, including white matter. However, the arterial transit time (δ_a) for white matter is not well established and a limited number of reports using multi‐delay methods have yielded inconsistent findings. In this study, we used a different approach and measured white matter δ_a (mean ± standard deviation, 1541 ± 173 ms) by determining the arrival times of exogenous contrast agent in a bolus tracking experiment. The data also confirmed δ_a of gray matter to be 912 ± 209 ms. In the second part of this study, we used these parameters in PCASL kinetic models and compared relative CBF (rCBF, with respect to the whole brain) maps with those measured using a single photon emission computed tomography (SPECT) technique. It was found that the use of tissue‐specific δ_a in the PCASL model was helpful in improving the correspondence between the two modalities. On a regional level, the gray/white matter CBF ratios were 2.47 ± 0.39 and 2.44 ± 0.18 for PCASL and SPECT, respectively. On a single‐voxel level, the variance between the modalities was still considerable, with an average rCBF difference of 0.27. Copyright © 2011 John Wiley & Sons, Ltd.     

Improved quantification of radionuclide uptake using deconvolution and windowed subtraction techniques for scatter compensation in single photon emission computed tomography

A comparison of two methods of scatter compensation in single photon emission computed tomography (SPECT) imaging is made on the basis of improvements in quantification. The methods, scatter-window subtraction and constrained deconvolution of an average point source response function (PSRF), are described; the theoretical basis of each method is also briefly assessed. Improvements in relative quantification offered by each method are measured by examining ratios of counts in hot cylinders to counts in a slightly radioactive background. The cylinder/background concentration ratio was varied by a factor of five; the sizes of the cylinders remained constant. Keeping the diameter of the cylinders constant allowed for an assessment of the effect of concentration differences, without the conflicting effect of variation in the size of the hot source. Results showed that while both scatter-window subtraction and constrained deconvolution offer quantification improvements in the final image, the method of prereconstruction deconvolution of a planar PSRF from each planar projection is substantially more successful than either scatter-window subtraction or other methods of implementing the deconvolution procedure.