High accuracy multiple scatter modelling for 3D whole body PET

A new technique for modelling multiple-order Compton scatter which uses the absolute probabilities relating the image space to the projection space in 3D whole body PET is presented. The details considered in this work give a valuable insight into the scatter problem, particularly for multiple scatter. Such modelling is advantageous for large attenuating media where scatter is a dominant component of the measured data, and where multiple scatter may dominate the total scatter depending on the energy threshold and object size. The model offers distinct features setting it apart from previous research: (1) specification of the scatter distribution for each voxel based on the transmission data, the physics of Compton scattering and the specification of a given PET system; (2) independence from the true activity distribution; (3) in principle no scaling or iterative process is required to find the distribution; (4) explicit multiple scatter modelling; (5) no scatter subtraction or addition to the forward model when included in the system matrix used with statistical image reconstruction methods; (6) adaptability to many different scatter compensation methods from simple and fast to more sophisticated and therefore slower methods; (7) accuracy equivalent to that of a Monte Carlo model. The scatter model has been validated using Monte Carlo simulation (SimSET).     

A parallelizable compression scheme for Monte Carlo scatter system matrices in PET image reconstruction

Scatter correction techniques in iterative positron emission tomography (PET) reconstruction increasingly utilize Monte Carlo (MC) simulations which are very well suited to model scatter in the inhomogeneous patient. Due to memory constraints the results of these simulations are not stored in the system matrix, but added or subtracted as a constant term or recalculated in the projector at each iteration. This implies that scatter is not considered in the back-projector. The presented scheme provides a method to store the simulated Monte Carlo scatter in a compressed scatter system matrix. The compression is based on parametrization and B-spline approximation and allows the formation of the scatter matrix based on low statistics simulations. The compression as well as the retrieval of the matrix elements are parallelizable. It is shown that the proposed compression scheme provides sufficient compression so that the storage in memory of a scatter system matrix for a 3D scanner is feasible. Scatter matrices of two different 2D scanner geometries were compressed and used for reconstruction as a proof of concept. Compression ratios of 0.1% could be achieved and scatter induced artifacts in the images were successfully reduced by using the compressed matrices in the reconstruction algorithm.     

Acceleration of Monte Carlo-based scatter compensation for cardiac SPECT

Single proton emission computed tomography (SPECT) images are degraded by photon scatter making scatter compensation essential for accurate reconstruction. Reconstruction-based scatter compensation with Monte Carlo (MC) modelling of scatter shows promise for accurate scatter correction, but it is normally hampered by long computation times. The aim of this work was to accelerate the MC-based scatter compensation using coarse grid and intermittent scatter modelling. The acceleration methods were compared to un-accelerated implementation using MC-simulated projection data of the mathematical cardiac torso (MCAT) phantom modelling (99m)Tc uptake and clinical myocardial perfusion studies. The results showed that when combined the acceleration methods reduced the reconstruction time for 10 ordered subset expectation maximization (OS-EM) iterations from 56 to 11 min without a significant reduction in image quality indicating that the coarse grid and intermittent scatter modelling are suitable for MC-based scatter compensation in cardiac SPECT.     

Iterative reconstruction methods for high-throughput PET tomographs

A fast iterative method is described for processing clinical PET scans acquired in three dimensions, that is, with no inter-plane septa, using standard computers to replace dedicated processors used until the late 1990s. The method is based on sinogram resampling, Fourier rebinning, Monte Carlo scatter simulation and iterative reconstruction using the attenuation-weighted OSEM method and a projector based on a Gaussian pixel model. Resampling of measured sinogram values occurs before Fourier rebinning, to minimize parallax and geometric distortions due to the circular geometry, and also to reduce the size of the sinogram. We analyse the geometrical and statistical effects of resampling, showing that the lines of response are positioned correctly and that resampling is equivalent to about 4 mm of post-reconstruction filtering. We also present phantom and patient results. In this approach, multi-bed clinical oncology scans can be ready for diagnosis within minutes.     

平行束单光子发射成像的定量解析重建

单光子发射断层成像技术在心血管及脑功能疾病的诊断上具有重要的临床意义。本研究以Kunyansky及以前的研究工作为基础，针对平行束探测模式，推导及建立了有效的解析重建算法，可对噪声、散射、衰减及探测器响应进行同时补偿，用于获取SPECT定量快速成像。数字及Monte Carlo仿真实验表明，所提出的定量解析重建算法是可行的，它极大地改善了重建图像的对比度及分辨率，基本消除了图像中的伪迹。该算法在达到迭代算法精度的同时，计算量却大为降低，与常规滤波反投影重建法近似。     

The influence of noise in full Monte Carlo ML-EM and dual matrix reconstructions in positron emission tomography

Monte Carlo (MC) simulations in positron emission tomography (PET) play an important role in detector modeling and algorithm testing. Whereas the simulations are widely used in a forward projection manner to accomplish this task, ideally they should be included into the reconstruction process itself. It is therefore desirable to investigate the convergence properties and the propagation of MC noise of these kinds of reconstruction algorithms. MC simulations were integrated into the maximum likelihood expectation maximization (ML-EM) algorithm in two different ways. In the full matrix approach the system matrix was calculated by running MC simulations, including scatter. This matrix was used in both the projector and the backprojector. In the dual matrix (DM) approach, MC simulations were used to incorporate scatter in the projector, whereas the backprojector only comprised attenuation. Repeated reconstructions with different MC seeds allowed a statistical analysis of the error at each iteration step and made it possible to investigate separately the propagation of the MC noise that was introduced by the sinogram, by the projector, and by the matrix. Both approaches resulted in similar images, but the DM approach with unmatched projector and backprojector yielded a faster initial convergence when compared to the ideal full matrix approach. The analysis of the noise sources for the modeled single ring scanner in full matrix reconstruction showed that the noise introduced by the matrix became comparable to the noise introduced by the sinogram when using a matrix that was simulated with 10,000 emissions/voxel.     

Fast hybrid SPECT simulation including efficient septal penetration modelling (SP-PSF)

Single photon emission computed tomography (SPECT) images are degraded by the detection of scattered photons and photons that penetrate the collimator septa. In this paper, a previously proposed Monte Carlo software that employs fast object scatter simulation using convolution-based forced detection (CFD) is extended towards a wide range of medium and high energy isotopes measured using various collimators. To this end, a fast method was developed for incorporating effects of septal penetrating (SP) photons. The SP contributions are obtained by calculating the object attenuation along the path from primary emission to detection followed by sampling a pre-simulated and scalable septal penetration point spread function (SP-PSF). We found that with only a very slight reduction in accuracy, we could accelerate the SP simulation by four orders of magnitude. To achieve this, we combined: (i) coarse sampling of the activity and attenuation distribution; (ii) simulation of the penetration only for a coarse grid of detector pixels followed by interpolation and (iii) neglection of SP-PSF elements below a certain threshold. By inclusion of this SP-PSF-based simulation it became possible to model both primary and septal penetrated photons while only 10% extra computation time was added to the CFD-based Monte Carlo simulator. As a result, a SPECT simulation of a patient-like distribution including SP now takes less than 5 s per projection angle on a dual processor PC. Therefore, the simulator is well-suited as an efficient projector for fully 3D model-based reconstruction or as a fast data-set generator for applications such as image processing optimization or observer studies.     

Correction for scatter and septal penetration using convolution subtraction methods and model-based compensation in 123I brain SPECT imaging-a Monte Carlo study

Scatter and septal penetration deteriorate contrast and quantitative accuracy in single photon emission computed tomography (SPECT). In this study four different correction techniques for scatter and septal penetration are evaluated for 123I brain SPECT. One of the methods is a form of model-based compensation which uses the effective source scatter estimation (ESSE) for modelling scatter, and collimator-detector response (CDR) including both geometric and penetration components. The other methods, which operate on the 2D projection images, are convolution scatter subtraction (CSS) and two versions of transmission dependent convolution subtraction (TDCS), one of them proposed by us. This method uses CSS for correction for septal penetration, with a separate kernel, and TDCS for scatter correction. The corrections are evaluated for a dopamine transporter (DAT) study and a study of the regional cerebral blood flow (rCBF), performed with 123I. The images are produced using a recently developed Monte Carlo collimator routine added to the program SIMIND which can include interactions in the collimator. The results show that the method included in the iterative reconstruction is preferable to the other methods and that the new TDCS version gives better results compared with the other 2D methods.     

An iterative three-dimensional electron density imaging algorithm using uncollimated compton scattered x rays from a polyenergetic primary pencil beam

X-ray film-screen mammography is currently the gold standard for detecting breast cancer. However, one disadvantage is that it projects a three-dimensional (3D) object onto a two-dimensional (2D) image, reducing contrast between small lesions and layers of normal tissue. Another limitation is its reduced sensitivity in women with mammographically dense breasts. Computed tomography (CT) produces a 3D image yet has had a limited role in mammography due to its relatively high dose, low resolution, and low contrast. As a first step towards implementing quantitative 3D mammography, which may improve the ability to detect and specify breast tumors, we have developed an analytical technique that can use Compton scatter to obtain 3D information of an object from a single projection. Imaging material with a pencil beam of polychromatic x rays produces a characteristic scattered photon spectrum at each point on the detector plane. A comparable distribution may be calculated using a known incident x-ray energy spectrum, beam shape, and an initial estimate of the object's 3D mass attenuation and electron density. Our iterative minimization algorithm changes the initially arbitrary electron density voxel matrix to reduce regular differences between the analytically predicted and experimentally measured spectra at each point on the detector plane. The simulated electron density converges to that of the object as the differences are minimized. The reconstruction algorithm has been validated using simulated data produced by the EGSnrc Monte Carlo code system. We applied the imaging algorithm to a cylindrically symmetric breast tissue phantom containing multiple inhomogeneities. A preliminary ROC analysis scores greater than 0.96, which indicate that under the described simplifying conditions, this approach shows promise in identifying and localizing inhomogeneities which simulate 0.5 mm calcifications with an image voxel resolution of 0.25 cm and at a dose comparable to mammography.     

A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor

A three-dimensional (3D) point-kernel multiple scatter model for point spread function (PSF) determination in parallel-beam single-photon emission computed tomography (SPECT), based on a dose gamma-ray buildup factor, is proposed. This model embraces nonuniform attenuation in a voxelized object of imaging (patient body) and multiple scattering that is treated as in the point-kernel integration gamma-ray shielding problems. First-order Compton scattering is done by means of the Klein-Nishina formula, but the multiple scattering is accounted for by making use of a dose buildup factor. An asset of the present model is the possibility of generating a complete two-dimensional (2D) PSF that can be used for 3D SPECT reconstruction by means of iterative algorithms. The proposed model is convenient in those situations where more exact techniques are not economical. For the proposed model's testing purpose calculations (for the point source in a nonuniform scattering object for parallel beam collimator geometry), the multiple-order scatter PSF generated by means of the proposed model matched well with those using Monte Carlo (MC) simulations. Discrepancies are observed only at the exponential tails mostly due to the high statistic uncertainty of MC simulations in this area, but not because of the inappropriateness of the model.     

Model-based crosstalk compensation for simultaneous 99mTc/123I dual-isotope brain SPECT imaging

In this work, we developed a model-based method to estimate and compensate for the crosstalk contamination in simultaneous 123I and 99mTc dual isotope brain single photo emission computed tomography imaging. The model-based crosstalk compensation (MBCC) includes detailed modeling of photon interactions inside both the object and the detector system. In the method, scatter in the object is modeled using the effective source scatter estimation technique, including contributions from all the photon emissions. The effects of the collimator-detector response, including the penetration and scatter components due to high-energy 123I photons, are modeled using precalculated tables of Monte Carlo simulated point-source response functions obtained from sources in air at various distances from the face of the collimator. The model-based crosstalk estimation method was combined with iterative reconstruction based compensation to reduce contamination due to crosstalk. The MBCC method was evaluated using Monte Carlo simulated and physical phantom experimentally acquired simultaneous dual-isotope data. Results showed that, for both experimental and simulation studies, the model-based method provided crosstalk estimates that were in good agreement with the true crosstalk. Compensation using MBCC improved image contrast and removed the artifacts for both Monte Carlo simulated and experimentally acquired data. The results were in good agreement with images acquired without any crosstalk contamination.     

Fully 3D iterative scatter-corrected OSEM for HRRT PET using a GPU

Accurate scatter correction is especially important for high-resolution 3D positron emission tomographies (PETs) such as high-resolution research tomograph (HRRT) due to large scatter fraction in the data. To address this problem, a fully 3D iterative scatter-corrected ordered subset expectation maximization (OSEM) in which a 3D single scatter simulation (SSS) is alternatively performed with a 3D OSEM reconstruction was recently proposed. However, due to the computational complexity of both SSS and OSEM algorithms for a high-resolution 3D PET, it has not been widely used in practice. The main objective of this paper is, therefore, to accelerate the fully 3D iterative scatter-corrected OSEM using a graphics processing unit (GPU) and verify its performance for an HRRT. We show that to exploit the massive thread structures of the GPU, several algorithmic modifications are necessary. For SSS implementation, a sinogram-driven approach is found to be more appropriate compared to a detector-driven approach, as fast linear interpolation can be performed in the sinogram domain through the use of texture memory. Furthermore, a pixel-driven backprojector and a ray-driven projector can be significantly accelerated by assigning threads to voxels and sinograms, respectively. Using Nvidia's GPU and compute unified device architecture (CUDA), the execution time of a SSS is less than 6 s, a single iteration of OSEM with 16 subsets takes 16 s, and a single iteration of the fully 3D scatter-corrected OSEM composed of a SSS and six iterations of OSEM takes under 105 s for the HRRT geometry, which corresponds to acceleration factors of 125× and 141× for OSEM and SSS, respectively. The fully 3D iterative scatter-corrected OSEM algorithm is validated in simulations using Geant4 application for tomographic emission and in actual experiments using an HRRT.     

Optimization of 2D image reconstruction for positron emission mammography using IDL

The Clear-PEM system is a prototype machine for Positron Emission Mammography (PEM) under development within the Portuguese PET-Mammography consortium. We have embedded 2D image reconstruction algorithms implemented in IDL within the prototype's image analysis package. The IDL implementation of these algorithms proved to be accurate and computationally efficient. In this paper, we present the implementation of the MLEM, OSEM and ART 2D iterative image reconstruction algorithms for PEM using IDL. C and IDL implementations are compared using realistic Monte Carlo simulated data. We show that IDL can be used for the easy implementation of image reconstruction algorithms for emission tomography.     

Scatter correction for positron emission mammography

In this paper we present a scatter correction method for a regularized list mode maximum likelihood reconstruction algorithm for the positron emission mammograph (PEM) that is being developed at our laboratory. The scatter events inside the object are modelled as additive Poisson random variables in the forward model of the reconstruction algorithm. The mean scatter sinogram is estimated using a Monte Carlo simulation program. With the assumption that the background activity is nearly uniform, the Monte Carlo scatter simulation only needs to run once for each PEM configuration. This saves computation time. The crystal scatters are modelled as a shift-invariant blurring in image domain because they are more localized. Thus, the useful information in the crystal scatters can be deconvolved in high-resolution reconstructions. The propagation of the noise from the estimated scatter sinogram into the reconstruction is analysed theoretically. The results provide an easy way to calculate the required number of events in the Monte Carlo scatter simulation for a given noise level in the image. The analysis is also applicable to other scatter estimation methods, provided that the covariance of the estimated scatter sinogram is available.     

Pragmatic fully 3D image reconstruction for the MiCES mouse imaging PET scanner

We present a pragmatic approach to image reconstruction for data from the micro crystal elements system (MiCES) fully 3D mouse imaging positron emission tomography (PET) scanner under construction at the University of Washington. Our approach is modelled on fully 3D image reconstruction used in clinical PET scanners, which is based on Fourier rebinning (FORE) followed by 2D iterative image reconstruction using ordered-subsets expectation-maximization (OSEM). The use of iterative methods allows modelling of physical effects (e.g., statistical noise, detector blurring, attenuation, etc), while FORE accelerates the reconstruction process by reducing the fully 3D data to a stacked set of independent 2D sinograms. Previous investigations have indicated that non-stationary detector point-spread response effects, which are typically ignored for clinical imaging, significantly impact image quality for the MiCES scanner geometry. To model the effect of non-stationary detector blurring (DB) in the FORE+OSEM(DB) algorithm, we have added a factorized system matrix to the ASPIRE reconstruction library. Initial results indicate that the proposed approach produces an improvement in resolution without an undue increase in noise and without a significant increase in the computational burden. The impact on task performance, however, remains to be evaluated.     

A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection

Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter form factor of the investigated object. Reconstruction from coherently scattered x-rays is commonly done using algebraic reconstruction techniques (ART). In this paper, we propose an alternative approach based on filtered back-projection. For the first time, a three-dimensional (3D) filtered back-projection technique using curved 3D back-projection lines is applied to two-dimensional coherent scatter projection data. The proposed algorithm is tested with simulated projection data as well as with projection data acquired with a demonstrator setup similar to a multi-line CT scanner geometry. While yielding comparable image quality as ART reconstruction, the modified 3D filtered back-projection algorithm is about two orders of magnitude faster. In contrast to iterative reconstruction schemes, it has the advantage that subfield-of-view reconstruction becomes feasible. This allows a selective reconstruction of the coherent-scatter form factor for a region of interest. The proposed modified 3D filtered back-projection algorithm is a powerful reconstruction technique to be implemented in a CSCT scanning system. This method gives coherent scatter CT the potential of becoming a competitive modality for medical imaging or nondestructive testing.     

3D reconstruction for a multi-ring PET scanner by single-slice rebinning and axial deconvolution

A three-dimensional (3D) image reconstruction method, which was originally developed for a positron emission tomography (PET) system consisting of two rotating scintillation cameras, has now been implemented for a multi-ring PET scanner with retractable septa. The method is called 'single-slice rebinning with axial deconvolution' (SSAD), and can be described as follows. The projection data are sorted into transaxial 2D sinograms. Correction for the axial blurring is made by deconvolution in the sinograms. To obtain the axial spread functions, which depend on the activity distribution, 2D reconstruction is first made using a limited axial acceptance angle. The final 3D image is obtained by 2D reconstruction of transaxial planes. The method is simple but not approximate, has a modest memory requirement, and can be combined with different 2D techniques. Evaluations by Monte Carlo simulations and phantom studies have been made.     

A slice-by-slice blurring model and kernel evaluation using the Klein-Nishina formula for 3D scatter compensation in parallel and converging beam SPECT

Converging collimation increases the geometric efficiency for imaging small organs, such as the heart, but also increases the difficulty of correcting for the physical effects of attenuation, geometric response and scatter in SPECT. In this paper, 3D first-order Compton scatter in non-uniform scattering media is modelled by using an efficient slice by-slice incremental blurring technique in both parallel and converging beam SPECT. The scatter projections are generated by first forming an effective scatter source image (ESSI), then forward-projecting the ESSI. The Compton scatter cross section described by the Klein-Nishina formula is used to obtain spatial scatter response functions (SSRFs) of scattering slices which are parallel to the detector surface. Two SSRFs of neighbouring scattering slices are used to compute two small orthogonal 1D blurring kernels used for the incremental blurring from the slice which is further from the detector surface to the slice which is closer to the detector surface. First-order Compton scatter point response functions (SPRFs) obtained using the proposed model agree well with those of Monte Carlo (MC) simulations for both parallel and fan beam SPECT. Image reconstruction in fan beam SPECT MC simulation studies shows increased left ventricle myocardium-to-chamber contrast (LV contrast) and slightly improved image resolution when performing scatter compensation using the proposed model. Physical torso phantom fan beam SPECT experiments show increased myocardial uniformity and image resolution as well as increased LV contrast. The proposed method efficiently models the 3D first-order Compton scatter effect in parallel and converging beam SPECT.