3D RBI-EM reconstruction with spherically-symmetric basis function for SPECT rotating slat collimator

A single photon emission computed tomography (SPECT) rotating slat collimator with strip detector acquires distance-weighted plane integral data, along with the attenuation factor and distance-dependent detector response. In order to image a 3D object, the slat collimator device has first to spin around its axis and then rotate around the object to produce 3D projection measurements. Compared to the slice-by-slice 2D reconstruction for the parallel-hole collimator and line integral data, a more complex 3D reconstruction is needed for the slat collimator and plane integral data. In this paper, we propose a 3D RBI-EM reconstruction algorithm with spherically-symmetric basis function, also called 'blobs', for the slat collimator. It has a closed and spherically symmetric analytical expression for the 3D Radon transform, which makes it easier to compute the plane integral than the voxel. It is completely localized in the spatial domain and nearly band-limited in the frequency domain. Its size and shape can be controlled by several parameters to have desired reconstructed image quality. A mathematical lesion phantom study has demonstrated that the blob reconstruction can achieve better contrast-noise trade-offs than the voxel reconstruction without greatly degrading the image resolution. A real lesion phantom study further confirmed this and showed that a slat collimator with CZT detector has better image quality than the conventional parallel-hole collimator with NaI detector. The improvement might be due to both the slat collimation and the better energy resolution of the CZT detector.     

Joint optimization of collimator and reconstruction parameters in SPECT imaging for lesion quantification

Obtaining the best possible task performance using reconstructed SPECT images requires optimization of both the collimator and reconstruction parameters. The goal of this study is to determine how to perform this optimization, namely whether the collimator parameters can be optimized solely from projection data, or whether reconstruction parameters should also be considered. In order to answer this question, and to determine the optimal collimation, a digital phantom representing a human torso with 16 mm diameter hot lesions (activity ratio 8:1) was generated and used to simulate clinical SPECT studies with parallel-hole collimation. Two approaches to optimizing the SPECT system were then compared in a lesion quantification task: sequential optimization, where collimation was optimized on projection data using the Cramer–Rao bound, and joint optimization, which simultaneously optimized collimator and reconstruction parameters. For every condition, quantification performance in reconstructed images was evaluated using the root-mean-squared-error of 400 estimates of lesion activity. Compared to the joint-optimization approach, the sequential-optimization approach favoured a poorer resolution collimator, which, under some conditions, resulted in sub-optimal estimation performance. This implies that inclusion of the reconstruction parameters in the optimization procedure is important in obtaining the best possible task performance; in this study, this was achieved with a collimator resolution similar to that of a general-purpose (LEGP) collimator. This collimator was found to outperform the more commonly used high-resolution (LEHR) collimator, in agreement with other task-based studies, using both quantification and detection tasks.     

An analytical reconstruction algorithm for multifocal converging-beam SPECT

Multifocal converging-beam collimation has been suggested for cardiac SPECT imaging to increase sensitivity over the heart without truncation of the activity distribution in the chest. In this study, an analytical reconstruction algorithm is derived for multifocal fan-beam and multifocal cone-beam tomography. In the algorithm, the projection data are differently weighted and filtered, depending on the distance from the detector. For a given image point, the set of filtered data corresponding to the distance between this point and detector is backprojected to determine the pixel value of the point. Thus, the backprojection is done only once at each projection view. To evaluate the algorithm, simulation studies are performed using a 3D Defrise slab phantom without considering photon attenuation and scatter, detector response, and statistical noise. Reconstructed images demonstrate that reasonable quality can be achieved with a modest focal-length variation rate and with a small radius of rotation. A collimator with a focal length increasing quickly near its centre provides better quality in the image region distant from the central plane of the cone geometry, but produces more severe artifacts at the centre of the reconstructed image, compared to a collimator with an initially slowly varying focal length.     

OSEM重建算法中几个关键问题的研究

目的：改进平行孔准直器SPECT系统的成像方法，快速、精确地实现有序子集期望值最大化（OSEM）重建算法。方法：采用理想平行孔和张角效应平行孔准直器两种模型，将准直器的空间响应融入系统传输矩阵，利用改进的射线跟踪算法进行衰减校正。结果：随着准直器张角的增加，Jaszczak模型的重建图像在边界出现明显的亮环；利用考虑准直器空间响应的系统矩阵进行图像重建．能较好的抑制边界伪影。结论：融入准直器空间响应函数的系统矩阵更为精确、贴近真实情况，能较好的抑制边界伪影，提高了重建图像的对比度和信噪比。     

Resolution recovery for list-mode reconstruction in SPECT

The purpose of the study was to evaluate the resolution recovery in the list-mode iterative reconstruction algorithm (LMIRA) for SPECT. In this study we compare the performance of the proposed method with other iterative resolution recovery methods for different noise levels. We developed an iterative reconstruction method which uses list-mode data instead of binned data. The new algorithm makes use of a more accurate model of the collimator structure. We compared the SPECT list-mode reconstruction with MLEM, OSEM and RBI, all including resolution recovery. For the evaluation we used Gaussian shaped sources with different FWHM at three different locations and three noise levels. For these distributions we calculated the reconstructed images for a different number of iterations. The absolute error for the reconstructed images was used to evaluate the performance. The performance of all four methods is comparable for the sources located in the centre of the field of view. For the sources located out of the centre, the error of the list-mode method is significantly lower than that of the other methods. Splitting the system model into a separate object-dependent and detector-dependent module gives us a flexible reconstruction method. With this we can very easily adapt the resolution recovery to different collimator types.     

Experimental results from a prototype slit-slat collimator with mixed multiplexed and non-multiplexed data

We have previously shown with simulations that a gain in signal-to-noise ratio (SNR) can be obtained by using mixed multiplexed (MX) and non-MX data in a slit-slat SPECT system as compared to using non-MX data only. We have now developed a prototype slit-slat collimator for a conventional gamma camera in order to validate these simulation results. The prototype collimator consists of seven slits and multiple parallel slats. Image reconstruction is performed using a modified OSEM algorithm, which takes into account geometric sensitivity variations and attenuation, but not scatter or resolution effects. Here, we first describe the calibration of the system and then we present the experimental validation with phantom experiments. SPECT acquisitions using different geometric and anthropomorphic phantoms were performed with and without multiplexing. The results show that reconstruction of the MX projections with the non-MX-projections eliminates artefacts caused by multiplexing. SNR gains obtained using the mixed MX and non-MX configurations were in the range of 26% to 51% for different phantoms. The results were in agreement with our previously published simulation work, proving that combining MX and non-MX data can result in artefact-free reconstructed images with improved SNR.     

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.     

Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

A rotating slat collimator can be used to acquire planar-integral data. It achieves higher geometric efficiency than a parallel-hole collimator by accepting more photons, but the planar-integral data contain less tomographic information that may result in larger noise amplification in the reconstruction. Lodge evaluated the rotating slat system and the parallel-hole system based on noise behavior for an FBP reconstruction. Here, we evaluate the noise propagation properties of the two collimation systems for iterative reconstruction. We extend Huesman's noise propagation analysis of the line-integral system to the planar-integral case, and show that approximately 2.0(D/dp) SPECT angles, 2.5(D/dp) self-spinning angles at each detector position, and a 0.5dp detector sampling interval are required in order for the planar-integral data to be efficiently utilized. Here, D is the diameter of the object and dp is the linear dimension of the voxels that subdivide the object. The noise propagation behaviors of the two systems are then compared based on a least-square reconstruction using the ratio of the SNR in the image reconstructed using a planar-integral system to that reconstructed using a line-integral system. The ratio is found to be proportional to the square root of F/D, where F is a geometric efficiency factor. This result has been verified by computer simulations. It confirms that for an iterative reconstruction, the noise tradeoff of the two systems is not only dependent on the increase of the geometric efficiency afforded by the planar projection method, but also dependent on the size of the object. The planar-integral system works better for small objects, while the line-integral system performs better for large ones. This result is consistent with Lodge's results based on the FBP method.     

Noise characteristics for cone beam collimators: a comparison with parallel hole collimator

In order to evaluate the properties of a cone beam (CB) collimator and three-dimensional filtered backprojection algorithm, the noise characteristics of this collimator configuration were determined and comparisons with a parallel hole (PH) collimator were made. Noise characteristics were evaluated using two approaches: the first consisted of assessing the magnitude of local random fluctuations in the reconstructed images, and the second consisted of assessing the noise texture in these images in the frequency domain by evaluating the noise power spectrum. Data used for these measurements were simulated using Monte Carlo models of SPECT systems equipped with cone beam and parallel hole collimators. Finally, to compare experimentally a specially designed high resolution CB collimator with a high resolution (HRES) PH collimator, measurements of a physical phantom were performed. Results of our studies show better noise magnitude for CB collimators; however, for CB collimators with short focal lengths (40-60 cm) the shape of %RMS noise distributions differs from slice to slice.     

Implementation of an iterative scatter correction, the influence of attenuation map quality and their effect on absolute quantitation in SPECT

We investigated the accuracy of qSPECT, a quantitative SPECT reconstruction algorithm we have developed which employs corrections for collimator blurring, photon attenuation and scatter, and provides images in units of absolute radiotracer concentrations (kBq cm(-3)). Using simulated and experimental phantom data with characteristics similar to clinical cardiac perfusion data, we studied the implementation of a scatter correction (SC) as part of an iterative reconstruction protocol. Additionally, with experimental phantom studies we examined the influence of CT-based attenuation maps, relative to those obtained from conventional SPECT transmission scans, on SCs and quantitation. Our results indicate that the qSPECT estimated scatter corrections did not change appreciably after the third iteration of the reconstruction. For the simulated data, qSPECT concentrations agreed with images reconstructed using ideal, scatter-free, simulated data to within 6%. For the experimental data, we observed small systematic differences in the scatter fractions for data using different combinations of SCs and attenuation maps. The SCs were found to be significantly influenced by errors in image coregistration. The reconstructed concentrations using CT-based corrections were more quantitatively accurate than those using attenuation maps from conventional SPECT transmission scans. However, segmenting the attenuation maps from SPECT transmission scans could provide sufficient accuracy for most applications.     

Brain SPECT with short focal-length cone-beam collimation

Single-photon emission-computed tomography (SPECT) imaging of deep brain structures is compromised by loss of photons due to attenuation. We have previously shown that a centrally peaked collimator sensitivity function can compensate for this phenomenon, increasing sensitivity over most of the brain. For dual-head instruments, parallel-hole collimators cannot provide variable sensitivity without simultaneously degrading spatial resolution near the center of the brain; this suggests the use of converging collimators. We have designed collimator pairs for dual-head SPECT systems to increase sensitivity, particularly in the center of the brain, and compared the new collimation approach to existing approaches on the basis of performance in estimating activity concentration of small structures at various locations in the brain. The collimator pairs we evaluated included a cone-beam collimator, for increased sensitivity, and a fan-beam collimator, for data sufficiency. We calculated projections of an ellipsoidal uniform background, with 0.9-cm-radius spherical lesions at several locations in the background. From these, we determined ideal signal-to-noise ratios (SNRCRB) for estimation of activity concentration within the spheres, based on the Cramer-Rao lower bound on variance. We also reconstructed, by an ordered-subset expectation-maximization (OS-EM) procedure, images of this phantom, as well as of the Zubal brain phantom, to allow visual assessment and to ensure that they were free of artifacts. The best of the collimator pairs evaluated comprised a cone-beam collimator with 20 cm focal length, for which the focal point is inside the brain, and a fan-beam collimator with 40 cm focal length. This pair yielded increased SNRCRB, compared to the parallel-parallel pair, throughout the imaging volume. The factor by which SNRCRB increased ranged from 1.1 at the most axially extreme location to 3.5 at the center. The gains in SNRCRB were relatively robust to mismatches between the center of the brain and the center of the imaging volume. Artifact-free reconstructions of simulated data acquired using this pair were obtained. Combining fan-beam and short-focusing cone-beam collimation should greatly improve dual-head brain SPECT imaging, especially for centrally located structures.     

Monte Carlo modelling of the performance of a rotating slit-collimator for improved planar gamma-camera imaging.

Planar imaging with a gamma camera is currently limited by the performance of the collimator. Spatial resolution and sensitivity trade off against each other; it is not possible with conventional parallel-hole collimation to have high geometric sensitivity and at the same time excellent spatial resolution unless field-of-view is sacrificed by using fan- or cone-beam collimators. We propose a rotating slit-collimator which collects one-dimensional projections from which the planar image may be reconstructed by the theory of computed tomography. The performance of such a collimator is modelled by Monte Carlo methods and images are reconstructed by a convolution and backprojection technique. The performance is compared with that of a conventional parallel-hole collimator and it is shown that higher spatial resolution with increased sensitivity is possible with the slit-collimator. For a point source a spatial resolution of some 6 mm at a distance of 100 mm from the collimator with a x7 sensitivity compared with a parallel-hole collimator was achieved. Applications to bone scintigraphy are modelled and an improved performance in hot-spot imaging is demonstrated. The expected performance in cold-spot imaging is analytically investigated. The slit-collimator is not expected to improve cold-spot imaging. Practical design considerations are discussed.     

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.     

CdZnTe strip detector SPECT imaging with a slit collimator

In this paper, we propose a CdZnTe rotating and spinning gamma camera attached with a slit collimator. This imaging system acquires convergent planar integrals of a radioactive distribution. Two analytical image reconstruction algorithms are proposed. Preliminary phantom studies show that our small CdZnTe camera with a slit collimator outperforms a larger NaI(Tl) camera with a pinhole collimator in terms of spatial resolution in the reconstructed images. The main application of this system is small animal SPECT imaging.     

Quantitative reconstruction for myocardial perfusion SPECT: an efficient approach by depth-dependent deconvolution and matrix rotation

An efficient reconstruction method for myocardial perfusion single-photon emission computed tomography (SPECT) has been developed which compensates simultaneously for attenuation, scatter, and resolution variation. The scattered photons in the primary-energy-window measurements are approximately removed by subtracting the weighted scatter-energy-window samples. The resolution variation is corrected by deconvolving the subtracted data with the detector-response kernel in frequency space using the depth-dependent frequency relation. The attenuated photons are compensated by recursively tracing the attenuation factors through the object-specific attenuation map. An experimental chest phantom with defects inside myocardium was used to test the method. The attenuation map of the phantom was reconstructed from transmission scans using a flat external source and a high-resolution parallel-hole collimator of a single-detector system. The detector-response kernel was approximated from measurements of a point source in air at several depths from the collimator surface. The emission data were acquired by the same detector setting. A computer simulation using similar protocols as in the experiment was performed. Both the simulation and experiment showed significant improvement in quantification with the proposed method, as compared to the conventional filtered-backprojection technique. The quantitative gain by the additional deconvolution was demonstrated. The computation time was less than 20 min on a HP/730 desktop computer for reconstruction of a 1282 x 64 array from 128 projections of 128 x 64 samples.     

Cone beam collimation for single photon emission computed tomography: analysis, simulation, and image reconstruction using filtered backprojection

This paper presents an analysis of two cone beam configurations (having focal lengths of 40 and 60 cm) for the acquisition of single photon emission computed tomography (SPECT) projection data. A three-dimensional filtered backprojection algorithm is used to reconstruct SPECT images of cone beam projection data obtained using Monte Carlo simulations. The mathematical analysis resulted in on-axis point source sensitivities (calculated for a distance of 15 cm from the collimator surface) for cone beam configurations that were 1.4-3 times the sensitivities of parallel-hole and fan beam geometries having similar geometric resolutions. Cone beam collimation offers the potential for improved sensitivity for SPECT devices using large-field-of-view scintillation cameras.     

Whole-body single-photon emission computed tomography using dual, large-field-of-view scintillation cameras.

A whole-body single-photon emission computed tomography system (SPECT) consisting of two large-field-of-view scintillation cameras mounted on a rotatable gantry, a minicomputer and a display station has been designed, constructed and evaluated. In its usual mode of operation, eleven contiguous transverse sections, each 12.5 or 25 mm thick, are reconstructed from projection data acquired during a single, continuous 360 degree rotation lasting from 2 to 22 min. A generalised filtered and weighted backprojection algorithm is used to reconstruct data obtained with conventional parallel-hole collimators in the case of body scanning, or with specially designed fan beam collimators in the case of centrally positioned organs. A simple, yet effective, correction is used to compensate for the effects of gamma ray attenuation within the patient. In addition to providing transverse section images, the system is capable of simultaneous acquisition of opposed conventional scintigrams, the reconstruction of longitudinal section images, and the acquisition of gated cardiac transverse sections. Resolutions in the reconstructed images are typically 15 mm for body scans and 11 mm for brain scans, with only slight variations in sensitivity and resolution within the image. Phantoms and clinical data demonstrate that the SPECT system generates high quality section images while maintaining most of the flexibility of normal scintillation cameras, with the added advantage of dual heads.     

基于旋转准直器的锥形束CT散射矫正方法

针对锥形束CT（CBCT）图像质量受散射影响比较严重的情况,提出一种基于旋转准直器的CBCT散射矫正方法。该方法在射线源和模体之间放置一个圆形的旋转准直器,并通过准直器的旋转使透过准直器的射线不断沿轴向来回扫描,以获取整个容积图像的投影图像信息,然后利用投影图像的遮挡区域估计整幅图像的散射信息并将其从投影图像中去除,最后利用改进FDK算法重建图像。结果表明,与CBCT图像相比,散射矫正后的重建图像CBCT值的均方根误差从16.00%下降为1.18%,杯状伪影从14.005%下降为0.660%,峰值信噪比从16.959 4提高到31.450 0。CBCT图像质量得到明显提高。     

Comparison of pinhole collimator materials based on sensitivity equivalence

Pinhole SPECT often provides an excellent resolution sensitivity trade-off for radionuclide imaging compared to SPECT with parallel holes, particularly when imaging small experimental animals like rodents. High absorption pinhole materials are often chosen because of their low edge penetration and therefore good system resolution. Capturing more photons in the edges however results in decreased system sensitivity if the pinhole diameter remains the same, which may partly undo the beneficial effect on the resolution. In the search for an optimal trade-off we have compared pinhole projection data and reconstructed images of different materials with pinhole aperture diameters adjusted to obtain equal sensitivity. Monte Carlo calculations modeling the transmission, penetration and scattering of gamma radiation in single pinholes of uranium, gold, tungsten and lead were performed for a range of pinhole opening angles, diameters and gamma ray energies. In addition, reconstructed images of a hot rod phantom were determined for a multipinhole SPECT system and for a system that can image the 511 keV annihilation photons of positron emitting tracers with clustered pinholes. Our results indicate that, under the condition of equal sensitivity, tungsten and for SPECT also lead pinholes perform just as well as gold and uranium ones, indicating that a significant cost reduction can be achieved in pinhole collimator manufacturing while the use of rare or impractical materials can be avoided.     

Optimizing the acquisition time profile for a planar integral measurement system with a spinning slat collimator

This article considers a hypothetical imaging device with a spinning slat collimator that measures parallel-planar-integral data from an object. This device rotates around the object 180 degrees and stops at N positions uniformly distributed over this 180 degrees. At each stop, the device spins on its own axis 180 degrees and acquires measurements at M positions uniformly distributed over this 180 degrees. For a fixed total imaging time, an optimal distribution of the scanning time among the data measurement locations is searched by a nonlinear programming method: Nelder-Mead's simplex method. The optimal dwell time is approximately proportional to the weighting factor in the backprojector of the reconstruction algorithm. By using an optimal dwell-time profile, the reconstruction signal-to-noise ratio has a gain of 23%-24% for the filtered backprojection algorithm and a gain of 10%-18% for the iterative algorithms, compared with the situation when a constant dwell-time profile is used.