Noniterative compensation for the distance-dependent detector response and photon attenuation in SPECT imaging

Contemporary Cardiac SPECT Imaging-Innovations and Best Practices: An Information Statement from the American Society of Nuclear Cardiology

This information statement from the American Society of Nuclear Cardiology highlights advances in cardiac SPECT imaging and supports the incorporation of new technology and techniques in laboratories performing nuclear cardiology procedures. The document focuses on the application of the latest imaging protocols and the utilization of newer hardware and software options to perform high quality, state-of-the-art SPECT nuclear cardiology procedures. Recommendations for best practices of cardiac SPECT imaging are discussed, highlighting what imaging laboratories should be doing as the standard of care in 2018 to achieve optimal results (based on the ASNC 2018 SPECT guideline [Dorbala et al., J Nucl Cardiol. 2018. https://doi.org/10.1007/s12350-018-1283-y ]).

Comparison of image reconstruction techniques for optical projection tomography

We present a comparison of image reconstruction techniques for optical projection tomography. We compare conventional filtered back projection, sinogram filtering using the frequency-distance relationship (FDR), image deconvolution, and 2D point-spread-function-based iterative reconstruction. The latter three methods aim to remove the spatial blurring in the reconstructed image originating from the limited depth of field caused by the point spread function of the imaging system. The methods are compared based on simulated data, experimental optical projection tomography data of single fluorescent beads, and high-resolution optical projection tomography imaging of an entire zebrafish larva. We demonstrate that the FDR method performs poorly on data acquired with high numerical aperture optical imaging systems. We show that the deconvolution technique performs best on highly sparse data with low signal-to-noise ratio. The point-spread-function-based reconstruction method is superior for nonsparse objects and data of high signal-to-noise ratio.

Evaluation of a matched filter resolution recovery reconstruction algorithm for SPECT-CT imaging

AIM

The aim of our study was to assess improvements in spatial resolution and noise control from the application of the Astonish resolution recovery algorithm for single photon emission computed tomography imaging. Secondary aims were to compare acquisitions made with low-energy general purpose collimators with those obtained using low-energy high-resolution collimators in this context and evaluate the potential of a finer matrix to improve image quality further.

MATERIALS AND METHODS

A Tc-filled Jaszczak phantom with hot spheres was used to assess contrast and noise. A National Electrical Manufacturers Association triple line source single photon emission computed tomography resolution phantom was used to measure spatial resolution. Acquisitions were made using both low-energy high-resolution and low-energy general purpose collimators.

RESULTS

Compared with standard ordered subsets expectation maximization reconstructions, the resolution recovery algorithm resulted in a higher spatial resolution (8 vs. 14 mm full-width at half-maximum) leading to reduced partial volume effects in the smaller Jaszczak spheres. Higher image contrast was achieved alongside lower levels of noise. An edge enhancement artefact was observed in the resolution recovery corrected images. An overestimate of the target-to-background activity was also observed for the larger spheres.

CONCLUSION

The use of such an algorithm results in images characterized by increased spatial resolution and reduced noise. However, small sources of the order of 2-3 cm can be significantly overenhanced.

Super resolution SPECT reconstruction with non-uniform attenuation

In this paper, based on Novikov's explicit inversion formula for the attenuated Radon transform, we present a super resolution SPECT reconstruction algorithm with compensation for non-uniform attenuation. Unlike the former methods improving the medical image resolution via super resolution (SR) in the reconstructed image, the proposed method apply the SR algorithm in the low resolution (LR) sinogram, which needs only 1-D shift of the detector, and the PSF is easy to obtain. Simulation results show that our reconstruction algorithm is effective.

Quantification and reduction of the collimator-detector response effect in SPECT by applying a system model during iterative image reconstruction: a simulation study

BACKGROUND

Detector blurring and non-ideal collimation decrease the spatial resolution of the single-photon emission computed tomography (SPECT) images. Iterative reconstruction algorithms such as ordered subsets expectation maximization (OSEM) can incorporate degrading factors during reconstruction. We investigated the quantitative errors associated with poor SPECT resolution and evaluated the importance of two-dimensional (2D) and three-dimensional (3D) resolution recovery by modelling system response during iterative image reconstruction.

METHODS

Different phantoms consisted of the NURBS-based cardiac-torso (NCAT) liver phantom with small tumors, the Zubal brain phantom and the NCAT heart phantom were used in this study. Monte Carlo simulation was used to create SPECT projections. Gaussian functions were used to model collimator detector response (CDR). Modeled CDRs were applied during OSEM. Both noise-free and noisy projections were created.

RESULTS

Even with noise-free projections, conventional OSEM algorithm provided limited quantitative accuracy compared to both 2D and 3D resolution recovery. The 3D implementation of resolution recovery, however, yielded superior results compared to its 2D implementation. For the liver phantom, the ability to distinguish small tumors in both transverse and axial planes was improved. For the brain phantom, gray to white matter activity ratio was increased from 3.14 ± 0.04 in simple OSEM to 3.84 ± 0.06 in 3D OSEM. For the NCAT heart phantom, 3D resolution recovery, results in images with thinner wall and higher contrast for different noise levels.

CONCLUSION

There are considerable quantitative errors associated with CDR, especially when the size of the target is comparable with the spatial resolution of the system. Between different reconstruction algorithms, 3D OSEM that consider the 3D nature of CDR, improve both the visual quality and the quantitative accuracy of any SPECT studies.

Application of blind deblurring reconstruction technique to SPECT imaging

An SPECT image can be approximated as the convolution of the ground truth spatial radioactivity with the system point spread function (PSF). The PSF of an SPECT system is determined by the combined effect of several factors, including the gamma camera PSF, scattering, attenuation, and collimator response. It is hard to determine the SPECT system PSF analytically, although it may be measured experimentally. We formulated a blind deblurring reconstruction algorithm to estimate both the spatial radioactivity distribution and the system PSF from the set of blurred projection images. The algorithm imposes certain spatial-frequency domain constraints on the reconstruction volume and the PSF and does not otherwise assume knowledge of the PSF. The algorithm alternates between two iterative update sequences that correspond to the PSF and radioactivity estimations, respectively. In simulations and a small-animal study, the algorithm reduced image blurring and preserved the edges without introducing extra artifacts. The localized measurement shows that the reconstruction efficiency of SPECT images improved more than 50% compared to conventional expectation maximization (EM) reconstruction. In experimental studies, the contrast and quality of reconstruction was substantially improved with the blind deblurring reconstruction algorithm.

Dynamic single photon emission computed tomography--basic principles and cardiac applications

The very nature of nuclear medicine, the visual representation of injected radiopharmaceuticals, implies imaging of dynamic processes such as the uptake and wash-out of radiotracers from body organs. For years, nuclear medicine has been touted as the modality of choice for evaluating function in health and disease. This evaluation is greatly enhanced using single photon emission computed tomography (SPECT), which permits three-dimensional (3D) visualization of tracer distributions in the body. However, to fully realize the potential of the technique requires the imaging of in vivo dynamic processes of flow and metabolism. Tissue motion and deformation must also be addressed. Absolute quantification of these dynamic processes in the body has the potential to improve diagnosis. This paper presents a review of advancements toward the realization of the potential of dynamic SPECT imaging and a brief history of the development of the instrumentation. A major portion of the paper is devoted to the review of special data processing methods that have been developed for extracting kinetics from dynamic cardiac SPECT data acquired using rotating detector heads that move as radiopharmaceuticals exchange between biological compartments. Recent developments in multi-resolution spatiotemporal methods enable one to estimate kinetic parameters of compartment models of dynamic processes using data acquired from a single camera head with slow gantry rotation. The estimation of kinetic parameters directly from projection measurements improves bias and variance over the conventional method of first reconstructing 3D dynamic images, generating time-activity curves from selected regions of interest and then estimating the kinetic parameters from the generated time-activity curves. Although the potential applications of SPECT for imaging dynamic processes have not been fully realized in the clinic, it is hoped that this review illuminates the potential of SPECT for dynamic imaging, especially in light of new developments that enable measurement of dynamic processes directly from projection measurements.

High-resolution versus high-sensitivity SPECT imaging with geometric blurring compensation for various parallel-hole collimation geometries

Recent studies have shown that trading efficiency for improved resolution may be a good choice for small lesion detection, but utilizing collimator with high efficiency may be more favorable for cardiac single photon emission computed tomography (SPECT). This paper investigates the tradeoffs of geometric-blurring compensation for high-resolution (HR) and high-sensitivity (HS) SPECT imaging with various parallel-hole collimators in terms of noise reduction and resolution recovery. Five types of collimators were investigated and compared with a general all purpose collimator using computer simulations. It is shown that less noisy SPECT images can be achieved with unchanged spatial resolution using large collimator holes with blurring compensation. The optimal collimator hole found in the computer simulation is the one with a hole acceptance angle in the range from 6.3 degrees to 9.4 degrees. Phantom experiments with two cardiac-insert phantoms show that the resolution of the image obtained using the HS collimator can be successfully recovered by blurring compensation, and the image is less noisy compared to the one obtained using the HR collimator.

Compensating for Non-Stationary Blurring by Further Blurring and Deconvolution

In many imaging systems, the point spread function (PSF) is non-stationary. Usually a computation-intensive iterative algorithm is used to de-blur the non-stationary PSF. This paper presents a new idea of using a non-iterative method to compensate for the spatially variant PSF. This method first further blurs the image with a non-stationary kernel so that the resultant image has a stationary PSF, then deblurs the resultant image using an efficient decovolution technique. The proposed method is illustrated and implemented by SPECT (single photon emission computed tomography) applications.

Scatter and blurring compensation in inhomogeneous media using a postprocessing method

An efficient postprocessing method to compensate for the scattering and blurring effects in inhomogeneous medium in SPECT is proposed. A two-dimensional point spread function (2D-PSF) was estimated in the image domain to model the combination of these two physical effects. This 2D-PSF in the inhomogeneous medium is fitted with an asymmetric Gaussian function based on Monte Carlo simulation results. An efficient further blurring and deconvolution method was used to restore images from the spatially variant 2D-PSF kernel. The compensation is performed using a computer-simulated NCAT phantom and a flanged Jaszczak experimental phantom. The preliminary results demonstrate an improvement in image quality and quantity accuracy with increased image contrast (25% increase compared to uncompensated image) and decreased error (40% decrease compared to uncompensated image). This method also offers an alternative to compensate for scatter and blurring in a more time efficient manner compared to the popular iterative methods. The execution time for this efficient postprocessing method is only a few minutes, which is within the clinically acceptable range.

Resolution improvement in emission optical projection tomography

A new imaging technique called emission optical projection tomography (eOPT), essentially an optical version of single-photon emission computed tomography (SPECT), provides molecular specificity, resolution on the order of microns to tens of microns, and large specimen coverage ( approximately 1 cubic centimetre). It is ideally suited to gene expression studies in embryos. Reconstructed eOPT images suffer from blurring that worsens as the distance from the axis of rotation increases. This blur is caused in part by the defocusing of the lens' point-spread function, which increases with object distance from the focal plane. In this paper, we describe a frequency space filter based on the frequency-distance relationship of sinograms to deconvolve the distance-dependent point-spread function and exclude highly defocused data from the eOPT sinograms prior to reconstruction. The method is shown to reduce the volume at half-maximum of the reconstructed point-spread function to approximately 20% the original, and the volume at 10% maximum to approximately 6% the original. As an illustration, the visibility of fine details in the vasculature of a 9.5 day old mouse embryo is dramatically improved.

The variation of intrinsic spatial resolution across the UFOV of scintillation cameras

The aim of the present study was to investigate in detail the variation of the intrinsic spatial resolution across the useful field of view (UFOV) of gamma-cameras and to explore whether this variation could lead to observable effects in clinical images. Two gamma-cameras were used, without their collimators, to acquire 560 (99m)Tc point source images at different points across their UFOVs, in order to measure the intrinsic spatial resolution at each point. Possible clinical effects of the resolution variation were examined on images of a thyroid phantom using a LEHR collimator, acquired at different locations on the UFOV and at various distances from the collimator. The gamma-camera intrinsic resolution varied significantly across the UFOV, being generally lower at the central region and deteriorating at the edges. Pronounced local maxima and minima were found at points corresponding to the centers of the photomultiplier tubes (PMTs) and halfway in between. Maximum differences of more than 50% were observed between the points presenting the best and worst intrinsic resolution. Differences between neighboring points reached 17%. The effects of resolution variation were clearly observable on the thyroid phantom images. It was concluded that an appropriate correction algorithm might be necessary in order to correct for the variation of the intrinsic spatial resolution across the UFOV of gamma-cameras.

Incorporation of system resolution compensation (RC) in the ordered-subset transmission (OSTR) algorithm for transmission imaging in SPECT

In order to reconstruct attenuation maps with improved spatial resolution and quantitative accuracy, we developed an approximate method of incorporating system resolution compensation (RC) in the ordered-subset transmission (OSTR) algorithm for transmission reconstruction. Our method approximately models the blur caused by the finite intrinsic detector resolution, the nonideal source collimation and detector collimation. We derived the formulation using the optimization transfer principle as in the derivation of the OSTR algorithm. The formulation includes one forward-blur step and one back-blur step, which do not severely slow down reconstruction. The formulation could be applicable to various transmission geometries, such as point-source, line-source, and sheet-source systems. Through computer simulations of the MCAT phantom and transmission measurements of the air-filled Data Spectrum Deluxe single photo emission computed tomography (SPECT) Phantom on a system which employed a cone-beam geometry and a system which employed a scanning-line-source geometry, we showed that incorporation of RC increased spatial resolution and improved the quantitative accuracy of reconstruction. In simulation studies, attenuation maps reconstructed with RC correction improved the quantitative accuracy of emission reconstruction.

Iterative three-dimensional expectation maximization restoration of single photon emission computed tomography images: Application in striatal imaging

Single photon emission computed tomography imaging suffers from poor spatial resolution and high statistical noise. Consequently, the contrast of small structures is reduced, the visual detection of defects is limited and precise quantification is difficult. To improve the contrast, it is possible to include the spatially variant point spread function of the detection system into the iterative reconstruction algorithm. This kind of method is well known to be effective, but time consuming. We have developed a faster method to account for the spatial resolution loss in three dimensions, based on a postreconstruction restoration method. The method uses two steps. First, a noncorrected iterative ordered subsets expectation maximization (OSEM) reconstruction is performed and, in the second step, a three-dimensional (3D) iterative maximum likelihood expectation maximization (ML-EM) a posteriori spatial restoration of the reconstructed volume is done. In this paper, we compare to the standard OSEM-3D method, in three studies (two in simulation and one from experimental data). In the two first studies, contrast, noise, and visual detection of defects are studied. In the third study, a quantitative analysis is performed from data obtained with an anthropomorphic striatal phantom filled with 123-I. From the simulations, we demonstrate that contrast as a function of noise and lesion detectability are very similar for both OSEM-3D and OSEM-R methods. In the experimental study, we obtained very similar values of activity-quantification ratios for different regions in the brain. The advantage of OSEM-R compared to OSEM-3D is a substantial gain of processing time. This gain depends on several factors. In a typical situation, for a 128 x 128 acquisition of 120 projections, OSEM-R is 13 or 25 times faster than OSEM-3D, depending on the calculation method used in the iterative restoration. In this paper, the OSEM-R method is tested with the approximation of depth independent resolution. For the striatum this approximation is appropriate, but for other clinical situations we will need to include a spatially varying response. Such a response is already included in OSEM-3D.

Analytical reconstruction of deconvolved Fourier rebinned PET sinograms

Fully 3D PET data are often rebinned into 2D data sets in order to avoid computationally intensive fully 3D reconstruction. Then, conventional 2D reconstruction techniques are employed to obtain images from the rebinned data. In a common scenario, 2D filtered back projection (FBP) is applied to Fourier rebinned (FORE) data. This approach is suboptimal because FBP is based on an idealized mathematical model of the data and cannot account for the statistical structure of data and noise. FORE data contain some blur in all three dimensions in comparison to conventional 2D PET data. In this work, we propose methods for approximating this blur in the sinogram domain due to FORE through its point spread function (PSF). We also explore simple methods for deconvolving the rebinned data with this PSF to restore it to a more ideal state prior to FBP. Our results show that deconvolution of the approximate transaxial PSF yields no improvement. When low image noise levels are required for detection tasks, the deconvolution of the axial PSF does not provide adequate resolution or quantitative benefits to justify its application. When accurate quantitation is required and higher noise levels are acceptable, the deconvolution of the axial PSF leads to considerable gains (30%) in accuracy over conventional FORE+FBP at matched noise levels.

Fully 3D Monte Carlo reconstruction in SPECT: a feasibility study

In single photon emission computed tomography (SPECT) with parallel hole collimation, image reconstruction is usually performed as a set of bidimensional (2D) analytical or iterative reconstructions. This approach ignores the tridimensional (3D) nature of scatter and detector response function that affects the detected signal. To deal with the 3D nature of the image formation process, iterative reconstruction can be used by considering a 3D projector modelling the 3D spread of photons. In this paper, we investigate the value of using accurate Monte Carlo simulations to determine the 3D projector used in a fully 3D Monte Carlo (F3DMC) reconstruction approach. Given the 3D projector modelling all physical effects affecting the imaging process, the reconstruction problem is solved using the maximum likelihood expectation maximization (MLEM) algorithm. To validate the concept, three data sets were simulated and F3DMC was compared with two other 3D reconstruction strategies using analytical corrections for attenuation, scatter and camera point spread function. Results suggest that F3DMC improves spatial resolution, relative and absolute quantitation and signal-to-noise ratio. The practical feasibility of the approach on real data sets is discussed.

Evaluation of an efficient compensation method for quantitative fan-beam brain SPECT reconstruction

Fan-beam collimators are designed to improve the system sensitivity and resolution for imaging small objects such as the human brain and breasts in single photon emission computed tomography (SPECT). Many reconstruction algorithms have been studied and applied to this geometry to deal with every kind of degradation factor. This paper presents a new reconstruction approach for SPECT with circular orbit, which demonstrated good performance in terms of both accuracy and efficiency. The new approach compensates for degradation factors including noise, scatter, attenuation, and spatially variant detector response. Its uniform attenuation approximation strategy avoids the additional transmission scan for the brain attenuation map, hence reducing the patient radiation dose and furthermore simplifying the imaging procedure. We evaluate and compare this new approach with the well-established ordered-subset expectation-maximization iterative method, using Monte Carlo simulations. We perform quantitative analysis with regional bias-variance, receiver operating characteristics, and Hotelling trace studies for both methods. The results demonstrate that our reconstruction strategy has comparable performance with a significant reduction of computing time.

Performance evaluation of OSEM reconstruction algorithm incorporating three-dimensional distance-dependent resolution compensation for brain SPECT: a simulation study

Iterative reconstruction techniques such as an ordered subsets-expectation maximization (OSEM) algorithm can easily incorporated various physical models of attenuation or scatter. We implemented OSEM reconstruction algorithm incorporating compensation for distance-dependent blurring due to the collimator in SPECT. The algorithm was examined by computer simulation to estimate the accuracy for brain perfusion study.

METHODS

The detector response was assumed to be a two-dimensional Gauss function and the width of the function varied linearly with the source-to-detector distance. The attenuation compensation (AC) was also included. To investigate the properties of the algorithm, we performed computer simulations with the point source and digital brain phantoms. In the point source phantom, the uniformity of FWHM for the radial, tangential and longitudinal directions was evaluated on the reconstruction image. As for the brain phantom, quantitative accuracy was estimated by comparing the reconstructed images with the true image by the mean square error (MSE) and the ratio of gray and white matter counts (G/W). Both noise free and noisy simulations were examined.

RESULTS

In the point source simulation, FWHM in radial, tangential and longitudinal directions were 14.7, 14.7 and 15.0 mm at the image center and were 15.9, 9.83 and 10.6 mm at a distance of 15 cm from the center by using FBP, respectively. On the other hand, they were 8.12, 8.12 and 7.83 mm at the image center, and were 7.45, 7.44 and 7.01 mm at 15 cm from the center by OSEM with distance-dependent resolution compensation (DRC). An isotropic and stationary resolution was obtained at any location by OSEM with DRC. The spatial resolution was also improved about 6.5 mm by OSEM with DRC at the image center. In the brain phantom simulation, the blurring at the edge of the brain structure was eliminated by using OSEM with both DRC and AC. The G/W was 2.95 and 2.68 for noise free and noisy cases, respectively, when no compensation was performed. But the values for G/W without and with noise became 3.45 and 3.21 with AC only and were improved to 3.75 and 3.71 with both AC and DRC. The G/W approached the true value (4.00) by using OSEM with both AC and DRC even when there was statistical noise.

CONCLUSION

In conclusion, OSEM reconstruction including the distance-dependent resolution compensation algorithm was reasonably successful in achieving isotropic and stationary resolution and improving the quantitative accuracy for brain perfusion SPECT.

A three-dimensional ray-driven attenuation, scatter and geometric response correction technique for SPECT in inhomogeneous media

The qualitative and quantitative accuracy of SPECT images is degraded by physical factors of attenuation, Compton scatter and spatially varying collimator geometric response. This paper presents a 3D ray-tracing technique for modelling attenuation, scatter and geometric response for SPECT imaging in an inhomogeneous attenuating medium. The model is incorporated into a three-dimensional projector-backprojector and used with the maximum-likelihood expectation-maximization algorithm for reconstruction of parallel-beam data. A transmission map is used to define the inhomogeneous attenuating and scattering object being imaged. The attenuation map defines the probability of photon attenuation between the source and the scattering site, the scattering angle at the scattering site and the probability of attenuation of the scattered photon between the scattering site and the detector. The probability of a photon being scattered through a given angle and being detected in the emission energy window is approximated using a Gaussian function. The parameters of this Gaussian function are determined using physical measurements of parallel-beam scatter line spread functions from a non-uniformly attenuating phantom. The 3D ray-tracing scatter projector-backprojector produces the scatter and primary components. Then, a 3D ray-tracing projector-backprojector is used to model the geometric response of the collimator. From Monte Carlo and physical phantom experiments, it is shown that the best results are obtained by simultaneously correcting attenuation, scatter and geometric response, compared with results obtained with only one or two of the three corrections. It is also shown that a 3D scatter model is more accurate than a 2D model. A transmission map is useful for obtaining measurements of attenuation and scatter in SPECT data, which can be used together with a model of the geometric response of the collimator to obtain corrected images with quantitative and diagnostically accurate information.

Non-iterative methods incorporating a priori source distribution and data information for suppression of image noise and artefacts in 3D SPECT

Non-iterative methods have been developed for image reconstruction in 3D SPECT with uniform attenuation and distance-dependent spatial resolution. It was observed that these methods can, in general, be susceptible to data noise and other errors, yielding conspicuous image artefacts. In this work, we developed and evaluated a regularized inverse-filtering approach for effective suppression of noise and artefacts in 3D SPECT images without significantly compromising image resolution. The proposed approach allows the incorporation of a priori random image field and data information and can thus robustly control the degree of suppression of noise and artefacts in 3D SPECT images. Using computer simulations, we evaluated and compared quantitatively images reconstructed from data sets of various noise levels by the use of the proposed methods and the existing non-iterative methods. These numerical results clearly demonstrated that the proposed regularized inverse-filtering approach can effectively suppress image noise and artefacts that plague the existing non-iterative methods, thus yielding quantitatively more accurate 3D SPECT images. The proposed regularized inverse-filtering approach can also be generalized to other imaging modalities.

Combined corrections for attenuation, depth-dependent blur, and motion in cardiac SPECT: a multicenter trial

BACKGROUND

The diagnostic accuracy of cardiac single photon emission computed tomography (SPECT) is limited by image-degrading factors, such as heart or subject motion, depth-dependent blurring caused by the collimator, and photon scatter and attenuation. We developed correction approaches for motion, depth-dependent blur, and attenuation and performed a multicenter validation.

METHODS AND RESULTS

Motion was corrected both transversely and axially with a cross-correlation technique. Depth-dependent blurring was corrected by first back-projecting each projection and then applying a depth-dependent Wiener filter row by row. Attenuation was corrected with an iterative, nonuniform Chang algorithm, based on a transmission scan-generated attenuation map. We validated these approaches in 112 subjects, including 36 women (20 healthy volunteers, 8 angiographically normal patients, and 8 patients with coronary artery disease [CAD] found by means of angiography) and 76 men (23 healthy volunteers, 10 angiographically normal patients, and 43 patients with CAD found by means of angiography). Either technetium 99m or thallium 201 was used for emission; either gadolinium 153 or Tc-99m was used for transmission. Images were reconstructed and blindly interpreted with a 5-point scale for receiver operating characteristic analysis in 2 ways: motion correction plus a Butterworth filter, and combined motion and blur and attenuation corrections. The interpretation by means of consensus was for the overall presence of CAD and vascular territory. The receiver operating characteristic curves for overall presence and each of the 3 main coronary arteries were all shifted upward and to the left and had larger areas under the curve, for combined corrections compared with motion correction and Butterworth. Sensitivity/specificity for motion correction and Butterworth were 84/69, 64/71, 32/94, and 71/81 overall for the left anterior descending, the right coronary artery, and circumflex territories, respectively, compared with 88/92, 77/93, 50/97, and 74/95, respectively, for the combined corrections.

CONCLUSIONS

The proposed combined corrections for motion, depth-dependent blur, and attenuation significantly improve diagnostic accuracy, when compared with motion correction alone.

LROC analysis of detector-response compensation in SPECT

Localization ROC (LROC) observer studies examined whether detector response compensation (DRC) in ordered-subset, expectation-maximization (OSEM) reconstructions helps in the detection and localization of hot tumors. Simulated gallium (Ga-67) images of the thoracic region were used in the study. The projection data modeled the acquisition of attenuated 93- and 185-keV photons with a medium-energy parallel-hole collimator, but scatter was not modeled. Images were reconstructed with five strategies: 1) OSEM with no DRC; 2) OSEM preceded by restoration filtering; 3) OSEM with iterative DRC; 4) OSEM with an ideal DRC; and 5) filtered backprojection (FBP) with no DRC. All strategies included attenuation correction. There were four LROC studies conducted. In a study using a single tumor activity, the ideal DRC offered the best performance, followed by iterative DRC, restoration filtering, OSEM with no DRC, and FBP. Statistical significance at the 5% level was found between all pairs of strategies except for restoration filtering and OSEM with no DRC. A similar ranking was found for a more realistic study using multiple tumor activities. Additional studies considered the effects of OSEM iteration number and tumor activity on the detection improvement that iterative DRC offered with respect to OSEM with no DRC.

A multiresolution restoration method for cardiac SPECT imaging

In this study we present a multiresolution based method for restoring cardiac SPECT projections. Original projections were decomposed into a set of sub-band frequency images by using analyzing functions localized in both the space and frequency domain. This representation allows a simple denoising and restoration procedure by discarding high-frequency channels and performing inversion only in low frequencies. The method was evaluated in bull's eye reconstructions of a realistic cardiac chest phantom with a custom-made liver insert and 99mTc liver-to-heart activity ratios (LHAR) of 0:1, 1.5:1, 2.5:1, and 3.5:1. The cardiac phantom in free air was used as the reference standard. Reconstructions were performed by filtered backprojection using (1) no correction; (2) restoration without attenuation correction; (3) attenuation correction without restoration; and (4) restoration and attenuation correction. The attenuation correction was carried out with the Chang's method for one iteration. Results were compared with those obtained using an optimized prereconstruction Metz filter. Quantitative analysis was performed by calculating the normalized chi-square measure and mean +/- s.d. of bull's eye counts. In reconstructions with high liver activity (LHAR > 2), attenuation correction without restoration severely distorted the polar maps due to the spill-over of liver activity into the inferior myocardial wall. Both restoration methods when combined with an attenuation correction compensated this artifact and yielded uniform polar maps similar to that of the standard reference. There was no visual or quantitative difference between the performance of Metz filtering and multiresolution restoration. However, the main advantage of the multiresolution method is that it states a more concise and straightforward approach to the restoration problem. Multiresolution based methods does not require information about the object image or optimization processes, such as in conventional nuclear medicine restoration filters. In addition, the method is easy to implement using DFT techniques and potentially can be extended to noniterative spatially shift-invariant restorations in SPECT.

Quantitative cardiac SPECT in three dimensions: validation by experimental phantom studies

A mathematical framework for quantitative SPECT (single photon emission computed tomography) reconstruction of the heart is presented. An efficient simultaneous compensation approach to the reconstruction task is described. The implementation of the approach on a digital computer is delineated. The approach was validated by experimental data acquired from chest phantoms. The phantoms consisted of a cylindrical elliptical tank of Plexiglass, a cardiac insert made of Plexiglass, a spine insert of packed bone meal and lung inserts made of styrofoam beads alone. Water bags were added to simulate different body characteristics. Comparison between the quantitative reconstruction and the conventional FBP (filtered backprojection) method was performed. The FBP reconstruction had a poor quantitative accuracy and varied for different body configurations. Significant improvement in reconstruction accuracy by the quantitative approach was demonstrated with a moderate computing time on a currently available desktop computer. Furthermore, the quantitative reconstruction was robust for different body characteristics. Therefore, the quantitative approach has the potential for clinical use.

Comparison of frequency-distance relationship and Gaussian-diffusion-based methods of compensation for distance-dependent spatial resolution in SPECT imaging

The goal of this investigation was to compare resolution recovery versus noise level of two methods for compensation of distance-dependent resolution (DDR) in SPECT imaging. The two methods of compensation were restoration filtering based on the frequency-distance relationship (FDR) prior to iterative reconstruction, and modelling DDR in the projector/backprojector pair employed in iterative reconstruction. FDR restoration filtering was computationally faster than modelling the detector response in iterative reconstruction. Using Gaussian diffusion to model the detector response in iterative reconstruction sped up the process by a factor of 2.5 over frequency domain filtering in the projector/backprojector pair. Gaussian diffusion modelling resulted in a better resolution versus noise tradeoff than either FDR restoration filtering or solely modelling attenuation in the projector/backprojector pair of iterative reconstruction. For the pixel size investigated herein (0.317 cm), accounting for DDR in the projector/backprojector pair by Gaussian diffusion, or by applying a blurring function based on the distance from the face of the collimator at each distance, resulted in very similar resolution recovery and slice noise level.

Reducing the influence of the partial volume effect on SPECT activity quantitation with 3D modelling of spatial resolution in iterative reconstruction

Quantitative parameters such as the maximum and total counts in a volume are influenced by the partial volume effect. The magnitude of this effect varies with the non-stationary and anisotropic spatial resolution in SPECT slices. The objective of this investigation was to determine whether iterative reconstruction which includes modelling of the three-dimensional (3D) spatial resolution of SPECT imaging can reduce the impact of the partial volume effect on the quantitation of activity compared with filtered backprojection (FBP) techniques which include low-pass, and linear restoration filtering using the frequency distance relationship (FDR). The iterative reconstruction algorithms investigated were maximum-likelihood expectation-maximization (MLEM), MLEM with ordered subset acceleration (ML-OS), and MLEM with acceleration by the rescaled-block-iterative technique (ML-RBI). The SIMIND Monte Carlo code was used to simulate small hot spherical objects in an elliptical cylinder with and without uniform background activity as imaged by a low-energy ultra-high-resolution (LEUHR) collimator. Centre count ratios (CCRs) and total count ratios (TCRs) were determined as the observed counts over true counts. CCRs were unstable while TCRs had a bias of approximately 10% for all iterative techniques. The variance in the TCRs for ML-OS and ML-RBI was clearly elevated over that of MLEM, with ML-RBI having the smaller elevation. TCRs obtained with FDR-Wiener filtering had a larger bias (approximately 30%) than any of the iterative reconstruction methods but near stationarity is also reached. Butterworth filtered results varied by 9.7% from the centre to the edge. The addition of background has an influence on the convergence rate and noise properties of iterative techniques.

Projection space image reconstruction using strip functions to calculate pixels more "natural" for modeling the geometric response of the SPECT collimator

The spatially varying geometric response of the collimator-detector system in single photon emission computed tomography (SPECT) causes loss in resolution, shape distortions, reconstructed density nonuniformity, and quantitative inaccuracies. A projection space image reconstruction algorithm is used to correct these reconstruction artifacts. The projectors F use strip functions to calculate pixels more "natural" for modeling the two-dimensional (2-D) geometric response of the SPECT collimator transaxially to the axis of rotation. These projectors are defined by summing the intersection of an array of multiple strips rotated at equal angles to approximate the ideal system geometric response of the collimator. Two projection models were evaluated for modeling the system geometric response function. For one projector each strip is of equal weight, for the other projector a Gaussian weighting is used. Parallel beam and fan beam projections of a physical three-dimensional (3-D) Hoffman brain phantom and a Jaszczak cold rod phantom were used to evaluate the geometric response correction. Reconstructions were obtained by using the singular value decomposition (SVD) method and the iterative conjugate gradient algorithm to solve for q in the imaging equation FGq = p, where p is the projection measurement. The projector F included the new models for the geometric response, whereas, the backprojector G did not always model the geometric response in order to increase the computational speed. The final reconstruction was obtained by sampling the backprojection Gq at a discrete array of points. Reconstructions produced by the two proposed projectors showed improved resolution when compared against a unit-strip "natural" pixel model, the conventional image pixelized model with ray tracing to calculate the geometric response, and the filtered backprojection algorithm. When the reconstruction is displayed on fine grid points, the continuity and resolution of the image is preserved without the ring artifacts seen in the unit-strip "natural" pixel model. With present computing power, the geometric response correction using the proposed projection space reconstruction approach is not yet feasible for routine clinical use.

Exact and approximate rebinning algorithms for 3-D PET data

This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18 degrees axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard "exact" 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time.

Tomographic image reconstruction from optical projections in light-diffusing media

The recent developments in light generation and detection techniques have opened new possibilities for optical medical imaging, tomography, and diagnosis at tissue penetration depths of ~10 cm. However, because light scattering and diffusion in biological tissue are rather strong, the reconstruction of object images from optical projections needs special attention. We describe a simple reconstruction method for diffuse optical imaging, based on a modified backprojection approach for medical tomography. Specifically, we have modified the standard backprojection method commonly used in x-ray tomographic imaging to include the effects of both the diffusion and the scattering of light and the associated nonlinearities in projection image formation. These modifications are based primarily on the deconvolution of the broadened image by a spatially variant point-spread function that is dependent on the scattering of light in tissue. The spatial dependence of the deconvolution and nonlinearity corrections for the curved propagating ray paths in heterogeneous tissue are handled semiempirically by coordinate transformations. We have applied this method to both theoretical and experimental projections taken by parallel- and fan-beam tomography geometries. The experimental objects were biomedical phantoms with multiple objects, including in vitro animal tissue. The overall results presented demonstrate that image-resolution improvements by nearly an order of magnitude can be obtained. We believe that the tomographic method presented here can provide a basis for rapid, real-time medical monitoring by the use of optical projections. It is expected that such optical tomography techniques can be combined with the optical tissue diagnosis methods based on spectroscopic molecular signatures to result in a versatile optical diagnosis and imaging technology.

Influence of the assessment of defect severity and intravenous nitrate administration during tracer injection on the detection of viable hibernating myocardium with data-based quantitative technetium 99m-labeled sestamibi single-photon emission computed tomography

BACKGROUND

This study aimed to verify whether the assessment of defect severity and the infusion of nitrates during tracer injection improve the capability of data-based 99mTc-labeled sestamibi single-photon emission computed tomography (SPECT) to recognize hibernating myocardium.

METHODS AND RESULTS

Of 66 asynergic coronary territories in 40 patients with left ventricular dysfunction, 28 had postrevascularization functional recovery (hibernating) and 38 had unchanged dysfunction (fibrotic). Defect severity was lower in the hibernating than in the fibrotic territories on both baseline (p < 0.01) and nitrate SPECT (p < 0.002). Nitrate was superior to baseline SPECT to differentiate the hibernating from the fibrotic territories (sensitivity 96% vs 75%, p < 0.05; receiver-operating characteristic curve area 0.75 vs 0.63, p < 0.001) and to identify the patients with improved left ventricular ejection fraction (receiver-operating characteristic curve area 0.68 vs 0.58; p < 0.05).

CONCLUSIONS

The analysis of defect severity in combination with nitrate infusion clearly improves the value of 99mTc-labeled sestamibi SPECT for the recognition of hibernating myocardium and the prediction of postrevascularization recovery.

An analytical approach for compensation of non-uniform attenuation in cardiac SPECT imaging

Photon attenuation can reduce the diagnostic accuracy of cardiac SPECT imaging. Bellini et al have previously derived a mathematically exact method to compensate for attenuation in a uniform attenuator. Since the human thorax contains structures with differing attenuation properties, non-uniform attenuation compensation is required in cardiac SPECT. Given an estimate of the patient attenuation map, we show that the Bellini attenuation compensation method can be used in cardiac SPECT to provide a quantitatively accurate reconstruction of a central region in the image which includes the heart and surrounding soft tissue. Simulations using a mathematical cardiac-torso phantom were conducted to evaluate the Bellini method and to compare its performance to the ML-EM iterative algorithm, and to 180 degrees and 360 degrees filtered backprojection (FBP) with no attenuation compensation. 'Bulls-eye' polar maps and circumferential profiles showed that both the Bellini method and the ML-EM algorithm provided quantitatively accurate reconstructions of the myocardium, with a substantial reduction in attenuation-induced artifacts that were observed in the FBP images. The computational load required to implement the Bellini method is approximately equivalent to that required for one iteration of the ML-EM algorithm, thus it is suitable for routine clinical use.

Fourier correction for spatially variant collimator blurring in SPECT

In single-photon emission computed tomography (SPECT), projection data are acquired by rotating the photon detector around a patient, either in a circular orbit or in a noncircular orbit. The projection data of the desired spatial distribution of emission activity is blurred by the point-response function of the collimator that is used to define the range of directions of gamma-ray photons reaching the detector. The point-response function of the collimator is not spatially stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual distance-dependent point-response function by a spatially invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. A method is described here for distance-dependent preprocessing of SPECT projection data prior to image reconstruction. Based on the special distance-dependent characteristics of the Fourier coefficients of the sinogram, a spatially variant inverse filter can be developed to process the projection data in all views simultaneously. The algorithm is first derived from Fourier analysis of the projection data from the circular orbit geometry. For circular orbit projection data, experimental results from both simulated data and real phantom data indicate the potential of this method. It is shown that the spatial filtering method can be extended to the projection data from the noncircular orbit geometry. Experiments on simulated projection data from an elliptical orbit demonstrate correction of the spatially variant blurring and distortion in the reconstructed image caused by the noncircular orbit geometry.