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In clinical brain SPECT, correction for photon attenuation in the patient is essential to obtain images which provide quantitative information on the regional activity concentration per unit volume (kBq. ml − 1 ). This correction generally requires an attenuation map ( μ map) denoting the attenuation coefficient at each voxel which is often derived from a CT or MRI scan. However, such an additional scan is not always available and the method may suffer from registration errors. Therefore, we propose a SPECT-only-based strategy for μ map estimation that we apply to a stationary multi-pinhole clinical SPECT system (G-SPECT-I) for 99mTc-HMPAO brain perfusion imaging. The method is based on the use of a convolutional neural network (CNN) and was validated with Monte Carlo simulated scans. Data acquired in list mode was used to employ the energy information of both primary and scattered photons to obtain information about the tissue attenuation as much as possible. Multiple SPECT reconstructions were performed from different energy windows over a large energy range. Locally extracted 4D SPECT patches (three spatial plus one energy dimension) were used as input for the CNN which was trained to predict the attenuation coefficient of the corresponding central voxel of the patch. Results show that Attenuation Correction using the Ground Truth μ maps (GT-AC) or using the CNN estimated μ maps (CNN-AC) achieve comparable accuracy. This was confirmed by a visual assessment as well as a quantitative comparison; the mean deviation from the GT-AC when using the CNN-AC is within 1.8% for the standardized uptake values in all brain regions. Therefore, our results indicate that a CNN-based method can be an automatic and accurate tool for SPECT attenuation correction that is independent of attenuation data from other imaging modalities or human interpretations about head contours.

Planar molecular breast imaging (MBI) is rapidly gaining in popularity in diagnostic oncology. To add 3D capabilities, we introduce a novel molecular breast tomosynthesis (MBT) scanner concept based on multi-pinhole collimation. In our design, the patient lies prone with the pendant breast lightly compressed between transparent plates. Integrated webcams view the breast through these plates and allow the operator to designate the scan volume (e.g. a whole breast or a suspected region). The breast is then scanned by translating focusing multi-pinhole plates and NaI(Tl) gamma detectors together in a sequence that optimizes count yield from the volume-of-interest. With simulations, we compared MBT with existing planar MBI. In a breast phantom containing different lesions, MBT improved tumour-to-background contrast-to-noise ratio (CNR) over planar MBI by 12% and 111% for 4.0 and 6.0 mm lesions respectively in case of whole breast scanning. For the same lesions, much larger CNR improvements of 92% and 241% over planar MBI were found in a scan that focused on a breast region containing several lesions. MBT resolved 3.0 mm rods in a Derenzo resolution phantom in the transverse plane compared to 2.5 mm rods distinguished by planar MBI. While planar MBI cannot provide depth information, MBT offered 4.0 mm depth resolution. Our simulations indicate that besides offering 3D localization of increased tracer uptake, multi-pinhole MBT can significantly increase tumour-to-background CNR compared to planar MBI. These properties could be promising for better estimating the position, extend and shape of lesions and distinguishing between single and multiple lesions.

Ordered subsets expectation maximization (OS-EM) is widely used to accelerate image reconstruction in single photon emission computed tomography (SPECT). Speedup of OS-EM over maximum likelihood expectation maximization (ML-EM) is close to the number of subsets used. Although a high number of subsets can shorten reconstruction times significantly, it can also cause severe image artifacts such as improper erasure of reconstructed activity if projections contain few counts. We recently showed that such artifacts can be prevented by using a count-regulated OS-EM (CR-OS-EM) algorithm which automatically adapts the number of subsets for each voxel based on the estimated number of counts that the voxel contributed to the projections. While CR-OS-EM reached high speed-up over ML-EM in high-activity regions of images, speed in low-activity regions could still be very slow. In this work we propose similarity-regulated OS-EM (SR-OS-EM) as a much faster alternative to CR-OS-EM. SR-OS-EM also automatically and locally adapts the number of subsets, but it uses a different criterion for subset regulation: the number of subsets that is used for updating an individual voxel depends on how similar the reconstruction algorithm would update the estimated activity in that voxel with different subsets. Reconstructions of an image quality phantom and in vivo scans show that SR-OS-EM retains all of the favorable properties of CR-OS-EM, while reconstruction speed can be up to an order of magnitude higher in low-activity regions. Moreover our results suggest that SR-OS-EM can be operated with identical reconstruction parameters (including the number of iterations) for a wide range of count levels, which can be an additional advantage from a user perspective since users would only have to post-filter an image to present it at an appropriate noise level.

In recent years, breast imaging using radiolabelled molecules has attracted significant interest. Our group has proposed a multi-pinhole molecular breast tomosynthesis (MP-MBT) scanner to obtain 3D functional molecular breast images at high resolutions. After conducting extensive optimisation studies using simulations, we here present a first prototype of MP-MBT and evaluate its performance using physical phantoms. The MP-MBT design is based on two opposing gamma cameras that can image a lightly compressed pendant breast. Each gamma camera consists of a 250 × 150 mm2 detector equipped with a collimator with multiple pinholes focusing on a line. The NaI(Tl) gamma detector is a customised design with 3.5 mm intrinsic spatial resolution and high spatial linearity near the edges due to a novel light-guide geometry and the use of square PMTs. A volume-of-interest is scanned by translating the collimator and gamma detector together in a sequence that optimises count yield from the scan region. Derenzo phantom images showed that the system can reach 3.5 mm resolution for a clinically realistic 99mTc activity concentration in an 11-minute scan, while in breast phantoms the smallest spheres visible were 6 mm in diameter for the same scan time. To conclude, the experimental results of the novel MP-MBT scanner showed that the setup had sub-centimetre breast tumour detection capability which might facilitate 3D molecular breast cancer imaging in the future.

Scintillation gamma cameras based on low-noise electron multiplication (EM-)CCDs can reach high spatial resolutions. For further improvement of these gamma cameras, more insight is needed into how various parameters that characterize these devices influence their performance. Here, we use the Cramer-Rao lower bound (CRLB) to investigate the sensitivity of the energy and spatial resolution of an EM-CCD-based gamma camera to several parameters. The gamma camera setup consists of a 3 mm thick CsI(Tl) scintillator optically coupled by a fiber optic plate to the E2V CCD97 EM-CCD. For this setup, the position and energy of incoming gamma photons are determined with a maximum-likelihood detection algorithm. To serve as the basis for the CRLB calculations, accurate models for the depth-dependent scintillation light distribution are derived and combined with a previously validated statistical response model for the EM-CCD. The sensitivity of the lower bounds for energy and spatial resolution to the EM gain and the depth-of-interaction (DOI) are calculated and compared to experimentally obtained values. Furthermore, calculations of the influence of the number of detected optical photons and noise sources in the image area on the energy and spatial resolution are presented. Trends predicted by CRLB calculations agree with experiments, although experimental values for spatial and energy resolution are typically a factor of 1.5 above the calculated lower bounds. Calculations and experiments both show that an intermediate EM gain setting results in the best possible spatial or energy resolution and that the spatial resolution of the gamma camera degrades rapidly as a function of the DOI. Furthermore, calculations suggest that a large improvement in gamma camera performance is achieved by an increase in the number of detected photons or a reduction of noise in the image area. A large noise reduction, as is possible with a new generation of EM-CCD electronics, may improve the energy and spatial resolution by a factor of 1.5.

High spatial resolution γ-imaging can be achieved with scintillator readout by low-noise, fast, electron-multiplying charge-coupled devices (EMCCDs). Previously we have shown that false-positive events due to EMCCD noise can be rejected by using the sum signal from silicon photomultipliers (SiPMs) mounted on the sides of the scintillator. Here we launch a next generation hybrid CCD-SiPM camera that utilizes the individual SiPM signals and maximum likelihood estimation (MLE) pre-localization of events to discriminate between true and false events in CCD frames. In addition, SiPM signals are utilized for improved energy discrimination. The performance of this hybrid detector was tested for a continuous CsI:Tl crystal at 140 keV. With a pre-localization accuracy of 1.06 mm (full-width-at-half-maximum) attained with MLE the signal-to-background ratio (SBR) was improved by a factor of 5.9, 4.0 or 2.2 compared to the EMCCD-only readout, at the cost of rejecting, respectively, 47%, 9% or 4% of the events. Combining the pre-localization and SiPM energy estimation improved the energy resolution from 50% to (19 ± 3)% while maintaining the spatial resolution at 180 µm.

Detection of x-rays and gamma rays with high spatial resolution can be achieved with scintillators that are optically coupled to electron-multiplying charge-coupled devices (EMCCDs). These can be operated at typical frame rates of 50 Hz with low noise. In such a set-up, scintillation light within each frame is integrated after which the frame is analyzed for the presence of scintillation events. This method allows for the use of scintillator materials with relatively long decay times of a few milliseconds, not previously considered for use in photon-counting gamma cameras, opening up an unexplored range of dense scintillators. In this paper, we test CdWO₄ and transparent polycrystalline ceramics of Lu₂O₃:Eu and (Gd,Lu)₂O₃:Eu as alternatives to currently used CsI:Tl in order to improve the performance of EMCCD-based gamma cameras. The tested scintillators were selected for their significantly larger cross-sections at 140 keV ((99m)Tc) compared to CsI:Tl combined with moderate to good light yield. A performance comparison based on gamma camera spatial and energy resolution was done with all tested scintillators having equal (66%) interaction probability at 140 keV. CdWO₄, Lu₂O₃:Eu and (Gd,Lu)₂O₃:Eu all result in a significantly improved spatial resolution over CsI:Tl, albeit at the cost of reduced energy resolution. Lu₂O₃:Eu transparent ceramic gives the best spatial resolution: 65 µm full-width-at-half-maximum (FWHM) compared to 147 µm FWHM for CsI:Tl. In conclusion, these 'slow' dense scintillators open up new possibilities for improving the spatial resolution of EMCCD-based scintillation cameras.

Ultra-high-resolution SPECT images can be obtained with focused multipinhole collimators. Here we investigate the influence of unwanted high tracer uptake outside the scan volume on reconstructed tracer distributions inside the scan volume, for (99m)Tc-tetrofosmin myocardial perfusion scanning in mice. Simulated projections of a digital mouse phantom (MOBY) in a focusing multipinhole SPECT system (U-SPECT-II, MILabs, The Netherlands) were generated. With this system differently sized user-defined scan volumes can be selected, by translating the animal in 3D through the focusing collimators. Scan volume selections were set to (i) a minimal volume containing just the heart, acquired without translating the animal during scanning, (ii) a slightly larger scan volume as is typically applied for the heart, requiring only small XYZ translations during scanning, (iii) same as (ii), but extended further transaxially, and (iv) same as (ii), but extended transaxially to cover the full thorax width (gold standard). Despite an overall negative bias that is significant for the minimal scan volume, all selected volumes resulted in visually similar images. Quantitative differences in the reconstructed myocardium between gold standard and the results from the smaller scan volume selections were small; the 17 standardized myocardial segments of a bull's eye plot, normalized to the myocardial mean of the gold standard, deviated on average 6.0%, 2.5% and 1.9% for respectively the minimal, the typical and the extended scan volume, while maximum absolute deviations were respectively 18.6%, 9.0% and 5.2%. Averaged over ten low-count noisy simulations, the mean absolute deviations were respectively 7.9%, 3.2% and 1.9%. In low-count noisy simulations, the mean and maximum absolute deviations for the minimal scan volume could be reduced to respectively 4.2% and 12.5% by performing a short survey scan of the exterior activity and focusing the remaining scan time at the organ of interest. We conclude that reconstructed tracer distribution in the myocardium can be influenced by activity in surrounding organs when a too narrow scan volume is used. With slightly larger scan volumes this problem is adequately suppressed. This approach produced a smaller mean deviation and may be more effective than employing a narrow scan volume with an additional survey scan.

Gamma cameras based on charge-coupled devices (CCDs) coupled to continuous scintillation crystals can combine a good detection efficiency with high spatial resolutions with the aid of advanced scintillation detection algorithms. A previously developed analytical multi-scale algorithm (MSA) models the depth-dependent light distribution but does not take statistics into account. Here we present and validate a novel statistical maximum-likelihood algorithm (MLA) that combines a realistic light distribution model with an experimentally validated statistical model. The MLA was tested for an electron multiplying CCD optically coupled to CsI(Tl) scintillators of different thicknesses. For (99m)Tc imaging, the spatial resolution (for perpendicular and oblique incidence), energy resolution and signal-to-background counts ratio (SBR) obtained with the MLA were compared with those of the MSA. Compared to the MSA, the MLA improves the energy resolution by more than a factor of 1.6 and the SBR is enhanced by more than a factor of 1.3. For oblique incidence (approximately 45°), the depth-of-interaction corrected spatial resolution is improved by a factor of at least 1.1, while for perpendicular incidence the MLA resolution does not consistently differ significantly from the MSA result for all tested scintillator thicknesses. For the thickest scintillator (3 mm, interaction probability 66% at 141 keV) a spatial resolution (perpendicular incidence) of 147 µm full width at half maximum (FWHM) was obtained with an energy resolution of 35.2% FWHM. These results of the MLA were achieved without prior calibration of scintillations as is needed for many statistical scintillation detection algorithms. We conclude that the MLA significantly improves the gamma camera performance compared to the MSA.

Several new methods for determining the depth of interaction (DOI) of annihilation photons in monolithic scintillator detectors with single-sided, multi-pixel readout are investigated. The aim is to develop a DOI decoding method that allows for practical implementation in a positron emission tomography system. Specifically, calibration data, obtained with perpendicularly incident gamma photons only, are being used. Furthermore, neither detector modifications nor a priori knowledge of the light transport and/or signal variances is required. For this purpose, a clustering approach is utilized in combination with different parameters correlated with the DOI, such as the degree of similarity to a set of reference light distributions, the measured intensity on the sensor pixel(s) closest to the interaction position and the peak intensity of the measured light distribution. The proposed methods were tested experimentally on a detector comprised of a 20 mm x 20 mm x 12 mm polished LYSO: Ce crystal coupled to a 4 x 4 multi-anode photomultiplier. The method based on the linearly interpolated measured intensities on the sensor pixels closest to the estimated (x, y)-coordinate outperformed the other methods, yielding DOI resolutions between similar to 1 and similar to 4.5 mm FWHM depending on the DOI, the (x, y) resolution and the amount of reference data used.

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.

Block-iterative image reconstruction methods, such as ordered subset expectation maximization (OSEM), are commonly used to accelerate image reconstruction. In OSEM, the speed-up factor over maximum likelihood expectation maximization (MLEM) is approximately equal to the number of subsets in which the projection data are divided. Traditionally, each subset consists of a couple of projection views, and the more subsets are used, the more the solution deviates from MLEM solutions. We found for multi-pinhole single photon emission computed tomography (SPECT) that even moderate acceleration factors in OSEM lead to inaccurate reconstructions. Therefore, we introduce pixel-based ordered subset expectation maximization (POSEM), which is based on an alternative subset choice. Pixels in each subset are spread out regularly over projections and are spatially separated as much as possible. We validated POSEM for data acquired with a focusing multi-pinhole SPECT system. Performance was compared with traditional OSEM and MLEM for a rat total body bone scan, a gated mouse myocardial perfusion scan and a Defrise phantom scan. We found that POSEM can be operated at acceleration factors that are often an order of magnitude higher than in traditional OSEM.

Gamma cameras based on charge-coupled devices (CCDs) and micro-columnar CsI scintillators can reach high spatial resolutions. However, the gamma interaction probability of these scintillators is low (typically30% at 141 keV) due to the limited thickness of presently available micro-columnar scintillators. Continuous scintillators can improve the interaction probability but suffer from increased light spread compared to columnar scintillators. In addition, for both types of scintillators, gamma photons incident at an oblique angle reduce the spatial resolution due to the variable depth of interaction (DOI). To improve the spatial resolution and spectral characteristics of these detectors, we have developed a fast analytic scintillation detection algorithm that makes use of a depth-dependent light spread model and as a result is able to estimate the DOI in the scintillator. This algorithm, performing multi-scale frame analysis, was tested for an electron multiplying CCD (EM-CCD) optically coupled to CsI(Tl) scintillators of different thicknesses. For the thickest scintillator (2.6 mm) a spatial resolution of 148 microm full width half maximum (FWHM) was obtained with an energy resolution of 46% FWHM for perpendicularly incident gamma photons (interaction probability 61% at 141 keV). The multi-scale algorithm improves the spatial resolution up to 11%, the energy resolution up to 36% and the signal-to-background counts ratio up to 46% compared to a previously implemented algorithm that did not model the depth-dependent light spread. In addition, the multi-scale algorithm can accurately estimate DOI. As a result, degradation of the spatial resolution due to the variable DOI for gamma photons incident at a 45 degrees angle was improved from 2.0 10(3) to 448 microm FWHM. We conclude that the multi-scale algorithm significantly improves CCD-based gamma cameras as can be applied in future SPECT systems.

Charge-coupled devices (CCDs) coupled to scintillation crystals can be used for high-resolution imaging with x-rays and gamma rays. When the CCD images can be read out fast enough, the energy and interaction position of individual gamma quanta can be estimated by a real-time image analysis of the scintillation light flashes ('photon-counting mode'). The electron-multiplying CCD (EMCCD) is well suited for fast read out, since even at high frame rates it has extremely low read-out noise. Back-illuminated (BI) EMCCDs have much higher quantum efficiency than front-illuminated (FI) EMCCDs. Here we compare the spatial and energy resolution of gamma cameras based on FI and BI EMCCDs. The CCDs are coupled to a 1000 microm thick columnar CsI(Tl) crystal for the purpose of Tc-99m and I-125 imaging. Intrinsic spatial resolutions of 44 microm for I-125 and 49 microm for Tc-99m were obtained when using a BI EMCCD, which is an improvement by a factor of about 1.2-2 over the FI EMCCD. Furthermore, in the energy spectrum of the BI EMCCD, the I-125 signal could be clearly separated from the background noise, which was not the case for the FI EMCCD. The energy resolution of a BI EMCCD for Tc-99m was estimated to be approximately 36 keV, full width at half maximum, at 141 keV. The excellent results for the BI EMCCD encouraged us to investigate the cooling requirements for our setup. We have found that for the BI EMCCD, the spatial and energy resolution, as well as image noise, remained stable over a range of temperatures from -50 degrees C to -15 degrees C. This is a significant advantage over the FI EMCCD, which suffered from loss of spatial and especially energy resolution at temperatures as low as -40 degrees C. We conclude that the use of BI EMCCDs may significantly improve the imaging capabilities and the cost efficiency of CCD-based high-resolution gamma cameras.

X-ray CT images obtained with iterative reconstruction (IR) can be hampered by the so-called edge and aliasing artefacts, which appear as interference patterns and severe overshoots in the areas of sharp intensity transitions. Previously, we have demonstrated that these artefacts are caused by discretization errors during the projection simulation step in IR. Although these errors are inherent to IR, they can be adequately suppressed by reconstruction on an image grid that is finer than that typically used for analytical methods such as filtered back-projection. Two other methods that may prevent edge artefacts are: (i) smoothing the projections prior to reconstruction or (ii) using an image representation different from voxels; spherically symmetric Kaiser-Bessel functions are a frequently employed example of such a representation. In this paper, we compare reconstruction on a fine grid with the two above-mentioned alternative strategies for edge artefact reduction. We show that the use of a fine grid results in a more adequate suppression of artefacts than the smoothing of projections or using the Kaiser-Bessel image representation.

Statistical reconstruction methods offer possibilities of improving image quality as compared to analytical methods, but current reconstruction times prohibit routine clinical applications. To reduce reconstruction times we have parallelized a statistical reconstruction algorithm for cone-beam x-ray CT, the ordered subset convex algorithm (OSC), and evaluated it on a shared memory computer. Two different parallelization strategies were developed: one that employs parallelism by computing the work for all projections within a subset in parallel, and one that divides the total volume into parts and processes the work for each sub-volume in parallel. Both methods are used to reconstruct a three-dimensional mathematical phantom on two different grid densities. The reconstructed images are binary identical to the result of the serial (non-parallelized) algorithm. The speed-up factor equals approximately 30 when using 32 to 40 processors, and scales almost linearly with the number of cpus for both methods. The huge reduction in computation time allows us to apply statistical reconstruction to clinically relevant studies for the first time.

Statistical methods for image reconstruction such as maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurate modelling of the photon transport and noise. Statistical reconstruction is prohibitively slow when applied to clinical x-ray cone-beam CT due to the large data sets and the high number of iterations required for reconstructing high resolution images. One way to reduce the reconstruction time is to use ordered subsets of projections during the iterations, which has been successfully applied to fan-beam x-ray CT. In this paper, we quantitatively analyse the use of ordered subsets in concert with the convex algorithm for cone-beam x-ray CT reconstruction, for the case of circular acquisition orbits. We focus on the reconstructed image accuracy of a 3D head phantom. Acceleration factors larger than 300 were obtained with errors smaller than 1%, with the preservation of signal-to-noise ratio. Pushing the acceleration factor towards 600 by using an increasing number of subsets increases the reconstruction error up to 5% and significantly increases noise. The results indicate that the use of ordered subsets can be extremely useful for cone-beam x-ray CT.

Pinhole collimation can provide both higher sensitivity and resolution than parallel hole collimation when used to image small objects. When objects are placed close to the pinhole, small pinhole diameters combined with high-magnification pinhole geometries yield ultra high resolution images. With Monte Carlo (MC) calculations it is possible to simulate accurately a wide range of features of pinhole imaging. The aim of the present work is to accelerate MC simulations of pinhole SPECT projections. To achieve speed-up, forced detection (FD), a commonly used acceleration technique, is replaced by a kernel-based forced detection (KFD) step. In KFD, instead of tracing individual photons from the source or last scatter position to the detector, a position dependent kernel (point spread function (PSF)) is projected on the detector. The PSFs for channel and knife edge pinhole apertures model the penetration effects through the aperture material. For simulations, the PSFs are pre-calculated and stored in tables. The speed-up and accuracy achieved by using KFD were validated by means of digital phantoms. MC simulations with FD and with KFD converge to almost identical images. However, KFD converges to an equal image noise level one to four orders of magnitude faster than FD, depending on the number of photons simulated. A simulator accelerated by KFD could serve as a practical tool to improve iterative image reconstruction.

Imaging of Tc-99m labelled tracers is gaining popularity for detecting breast tumours. Recently, we proposed a novel design for molecular breast tomosynthesis (MBT) based on two sliding focusing multi-pinhole collimators that scan a modestly compressed breast. Simulation studies indicate that MBT has the potential to improve the tumour-to-background contrast-to-noise ratio significantly over state-of-the-art planar molecular breast imaging. The aim of the present paper is to optimize the collimator-detector geometry of MBT. Using analytical models, we first optimized sensitivity at different fixed system resolutions (ranging from 5 to 12 mm) by tuning the pinhole diameters and the distance between breast and detector for a whole series of automatically generated multi-pinhole designs. We evaluated both MBT with a conventional continuous crystal detector with 3.2 mm intrinsic resolution and with a pixelated detector with 1.6 mm pixels. Subsequently, full system simulations of a breast phantom containing several lesions were performed for the optimized geometry at each system resolution for both types of detector. From these simulations, we found that tumour-to-background contrast-to-noise ratio was highest for systems in the 7 mm to 10 mm system resolution range over which it hardly varied. No significant differences between the two detector types were found.

Statistical methods for image reconstruction such as the maximum likelihood expectation maximization are more robust and flexible than analytical inversion methods and allow for accurate modelling of the counting statistics and photon transport during acquisition of projection data. Statistical reconstruction is prohibitively slow when applied to clinical x-ray CT due to the large data sets and the high number of iterations required for reconstructing high-resolution images. Recently, however, powerful methods for accelerating statistical reconstruction have been proposed which, instead of accessing all projections simultaneously for updating an image estimate, are based on accessing a subset of projections at the time during iterative reconstruction. In this paper we study images generated by the convex algorithm accelerated by the use of ordered subsets (the OS convex algorithm (OSC)) for data sets with sizes, noise levels and spatial resolution representative of x-ray CT imaging. It is only in the case of extremely high acceleration factors (higher than 50, corresponding to fewer than 20 projections per subset), that areas with incorrect grey values appear in the reconstructed images, and that image noise increases compared with the standard convex algorithm. These image degradations can be adequately corrected for by running the final iteration of OSC with a reduced number of subsets. Even by applying such a relatively slow final iteration, OSC produces almost an equal resolution and lesion contrast as the standard convex algorithm, but more than two orders of magnitude faster.

Accurate simulation of scatter in projection data of single photon emission computed tomography (SPECT) is computationally extremely demanding for activity distribution in non-uniform dense media. This paper suggests how the computation time and memory requirements can be significantly reduced. First the scatter projection of a uniform dense object (P(SDSE)) is calculated using a previously developed accurate and fast method which includes all orders of scatter (slab-derived scatter estimation), and then P(SDSE) is transformed towards the desired projection P which is based on the non-uniform object. The transform of P(SDSE) is based on two first-order Compton scatter Monte Carlo (MC) simulated projections. One is based on the uniform object (P(u)) and the other on the object with non-uniformities (P(nu)). P is estimated by P = P(SDSE) P(nu)/P(u). A tremendous decrease in noise in P is achieved by tracking photon paths for P(nu) identical to those which were tracked for the calculation of P(u) and by using analytical rather than stochastic modelling of the collimator. The method was validated by comparing the results with standard MC-simulated scatter projections (P) of 99mTc and 201Tl point sources in a digital thorax phantom. After correction, excellent agreement was obtained between P and P. The total computation time required to calculate an accurate scatter projection of an extended distribution in a thorax phantom on a PC is a only few tens of seconds per projection, which makes the method attractive for application in accurate scatter correction in clinical SPECT. Furthermore, the method removes the need of excessive computer memory involved with previously proposed 3D model-based scatter correction methods.

SPECT projections are contaminated by scatter, resulting in reduced image contrast and quantitative errors. When tissue is present behind the source, some of the detected photons backscatter via this tissue. Particularly in dual-isotope SPECT and in combined emission-transmission SPECT, backscatter constitutes a major part of the down-scatter contamination in lower-energy windows. In this paper, the effects of backscatter material were investigated. Planar images of 99mTc and 201Tl line sources between varying numbers of Perspex slabs were analysed using the photopeak windows and various scatter windows. In the 99mTc photopeak window no significant change in total counts due to backscatter material was measured. In the 201Tl photopeak window an increase of about 10% in total counts was observed. In the scatter windows an even more explicit influence of backscatter material was measured. For instance, at a forward depth of 10 cm, total counts of a 99mTc source detected in the 72 keV window eventually doubled with increasing backscatter material, compared with the situation without backscatter material. The backscatter contribution plateaued when more than 5-10 cm of scatter material was placed behind the source. In conclusion, backscatter should be taken into account, particularly in model-based down-scatter correction methods in dual-isotope SPECT and combined emission-transmission SPECT.

Iterative reconstruction from single photon emission computed tomography (SPECT) data requires regularization to avoid noise amplification and edge artefacts in the reconstructed image. This is often accomplished by stopping the iteration process at a relatively low number of iterations or by post-filtering the reconstructed image. The aim of this paper is to develop a method to automatically select an optimal combination of stopping iteration number and filters for a particular imaging situation. To this end different error measures between the distribution of a phantom and a corresponding filtered SPECT image are minimized for different iteration numbers. As a study example, simulated data representing a brain study are used. For post-reconstruction filtering, the performance of 3D linear diffusion (Gaussian filtering) and edge preserving 3D nonlinear diffusion (Catté scheme) is investigated. For reconstruction methods which model the image formation process accurately, error measures between the phantom and the filtered reconstruction are significantly reduced by performing a high number of iterations followed by optimal filtering compared with stopping the iterative process early. Furthermore, this error reduction can be obtained over a wide range of iteration numbers. Only a negligibly small additional reduction of the errors is obtained by including spatial variance in the filter kernel. Compared with Gaussian filtering, Catté diffusion can further reduce the error in some cases. For the examples considered, using accurate image formation models during iterative reconstruction is far more important than the choice of the filter.

Effects of different scatter compensation methods incorporated in fully 3D iterative reconstruction are investigated. The methods are: (i) the inclusion of an 'ideal scatter estimate' (ISE); (ii) like (i) but with a noiseless scatter estimate (ISE-NF); (iii) incorporation of scatter in the point spread function during iterative reconstruction ('ideal scatter model', ISM); (iv) no scatter compensation (NSC); (v) ideal scatter rejection (ISR), as can be approximated by using a camera with a perfect energy resolution. The iterative method used was an ordered subset expectation maximization (OS-EM) algorithm. A cylinder containing small cold spheres was used to calculate contrast-to-noise curves. For a brain study, global errors between reconstruction and 'true' distributions were calculated. Results show that ISR is superior to all other methods. In all cases considered, ISM is superior to ISE and performs approximately as well as (brain study) or better than (cylinder data) ISE-NF. Both ISM and ISE improve contrast-to-noise curves and reduce global errors, compared with NSC. In the case of ISE, blurring of the scatter estimate with a Gaussian kernel results in slightly reduced errors in brain studies, especially at low count levels. The optimal Gaussian kernel size is strongly dependent on the noise level.