An Iterative Image Space Reconstruction Algorthm Suitable for Volume ECT

The trend in the design of scanners for positron emission computed tomography has traditionally been to improve the transverse spatial resolution to several millimeters while maintaining relatively coarse axial resolution (1-2 cm). Several scanners are being built with fine sampling in the axial as well as transverse directions, leading to the possibility of the true volume imaging. The number of possible coincidence pairs in these scanners is quite large. The usual methods of image reconstruction cannot handle these data without making approximations. It is computationally most efficient to reduce the size of this large, sparsely populated array by back-projecting the coincidence data prior to reconstruction. While analytic reconstruction techniques exist for back-projected data, an iterative algorithm may be necessary for those cases where the point spread function is spatially variant. A modification of the maximum likelihood algorithm is proposed to reconstruct these back-projected data. The method, the iterative image space reconstruction algorithm (ISRA), is able to reconstruct data from a scanner with a spatially variant point spread function in less time than other proposed algorithms. Results are presented for single-slice data, simulated and actual, from the PENN-PET scanner.     

Fully-3D PET image reconstruction using scanner-independent, adaptive projection data and highly rotation-symmetric voxel assemblies

For iterative, fully 3D positron emission tomography (PET) image reconstruction intrinsic symmetries can be used to significantly reduce the size of the system matrix. The precalculation and beneficial memory-resident storage of all nonzero system matrix elements is possible where sufficient compression exists. Thus, reconstruction times can be minimized independently of the used projector and more elaborate weighting schemes, e.g., volume-of-intersection (VOI), are applicable. A novel organization of scanner-independent, adaptive 3D projection data is presented which can be advantageously combined with highly rotation-symmetric voxel assemblies. In this way, significant system matrix compression is achieved. Applications taking into account all physical lines-of-response (LORs) with individual VOI projectors are presented for the Siemens ECAT HR+ whole-body scanner and the Siemens BrainPET, the PET component of a novel hybrid-MR/PET imaging system. Measured and simulated data were reconstructed using the new method with ordered-subset-expectation-maximization (OSEM). Results are compared to those obtained by the sinogram-based OSEM reconstruction provided by the manufacturer. The higher computational effort due to the more accurate image space sampling provides significantly improved images in terms of resolution and noise.     

Comparison of 3-D reconstruction with 3D-OSEM and with FORE+OSEM for PET

The combination of Fourier rebinning (FORE) and the ordered subsets expectation-maximization (OSEM), a fast statistical algorithm, appears as a promising alternative to the fully three-dimensional (3-D) iterative approach for clinical positron emission tomography (PET) data. In this paper, we evaluated the properties of FORE+OSEM and compared it with fully 3-D OSEM using both simulations and data acquired by commercial scanners. The aim is to determine to what extent the speed advantage of FORE+OSEM is paid for by a possible degradation of image quality in the case of noisy clinical PET data. A forward- and back-projection pair based on a line integral model was used in two-dimensional OSEM and 3-D OSEM (3D-OSEM) instead of a system matrix. Different variants of both approaches have been studied with simulations in terms of contrast-noise tradeoff. Two variants--FORE+OSEM with attenuation weighting (AW) [FORE+OSEM(AW)] and 3D-OSEM with attenuation-normalization weighting (ANSP) and a shifted-Poisson (SP) model [3D-OSEM(ANSP)]--were compared with measured phantom data and patient data. Based on the results from both simulations and measured data, we conclude that: 1) both attenuation (-normalization) weighting and the SP model improve the image quality but slow down the convergence and 2) despite its approximate nature, FORE+OSEM does not show apparent image degradation compared with 3D-OSEM for data with a noise level typical of a whole-body FDG scan.     

Fourier rebinning applied to multiplanar circular-orbit cone-beam SPECT

We study the application of Fourier rebinning methods to dual-planar cone-beam SPECT. Dual-planar cone-beam SPECT involves the use of a pair of dissimilar cone-beam collimators on a dual-camera SPECT system. Each collimator has its focus in a different axial plane. While dual-planar data is best reconstructed with fully three-dimensional (3-D) iterative methods, these methods are slow and have prompted a search for faster reconstruction techniques. Fourier rebinning was developed to estimate equivalent parallel projections from 3-D PET data, but it simply expresses a relationship between oblique projections taken in planes not perpendicular to the axis of rotation and direct projections taken in those that are. We find that it is possible to put cone-beam data in this context as well. The rebinned data can then be reconstructed using either filtered backprojection (FBP) or parallel iterative algorithms such as OS-EM. We compare the Feldkamp algorithm and fully 3-D OSEM reconstruction with Fourier-rebinned reconstructions on realistically-simulated Tc-99m HMPAO brain SPECT data. We find that the Fourier-rebinned reconstructions exhibit much less image noise and lower variance in region-of-interest (ROI) estimates than Feldkamp. Also, Fourier-rebinning followed by OSEM with nonuniform attenuation correction exhibits less bias in ROI estimates than Feldkamp with Chang attenuation correction. The Fourier-rebinned ROI estimates exhibit bias and variance comparable to those from fully 3-D OSEM and require considerably less processing time. However, in areas off the axis of rotation, the axial-direction resolution of FORE-reconstructed images is poorer than that of images reconstructed with 3-D OSEM. We conclude that Fourier rebinning is a practical and potentially useful approach to reconstructing data from dual-planar circular-orbit cone-beam systems.     

A stationary sampling scheme for multilayer positron tomographs

A stationary sampling scheme applicable to tomographic instruments incorporating two or more detector layers is described and tested. In this concept, the detectors in adjacent layers are angularly offset by half the interdetector distance. By reconstructing in one single slice all lines of response defined by two adjacent rings of detectors, a fourfold increase in the number of coincidence lines is obtained and a uniform sampling distance equal to one-quarter the interdetector spacing is achieved. Whereas this is obtained at the expense of a 100% degradation of the resolution in the axial direction, with the recent breed of PET (positron emission tomography) scanners using nearly square cross section detectors, the resolution loss may be tolerable in many situations. In addition, normal reconstruction of the individual coincidence planes is always possible. The sampling concept was investigated experimentally with the help of the Universite de Sherbrooke PET camera simulator.     

Exact rebinning methods for three-dimensional PET

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.     

Accurate event-driven motion compensation in high-resolution PET incorporating scattered and random events

With continuing improvements in spatial resolution of positron emission tomography (PET) scanners, small patient movements during PET imaging become a significant source of resolution degradation. This work develops and investigates a comprehensive formalism for accurate motion-compensated reconstruction which at the same time is very feasible in the context of high-resolution PET. In particular, this paper proposes an effective method to incorporate presence of scattered and random coincidences in the context of motion (which is similarly applicable to various other motion correction schemes). The overall reconstruction framework takes into consideration missing projection data which are not detected due to motion, and additionally, incorporates information from all detected events, including those which fall outside the field-of-view following motion correction. The proposed approach has been extensively validated using phantom experiments as well as realistic simulations of a new mathematical brain phantom developed in this work, and the results for a dynamic patient study are also presented.      

Fast, Accurate and Shift-Varying Line Projections for Iterative Reconstruction Using the GPU

List-mode processing provides an efficient way to deal with sparse projections in iterative image reconstruction for emission tomography. An issue often reported is the tremendous amount of computation required by such algorithm. Each recorded event requires several back- and forward line projections. We investigated the use of the programmable graphics processing unit (GPU) to accelerate the line-projection operations and implement fully-3D list-mode ordered-subsets expectation-maximization for positron emission tomography (PET). We designed a reconstruction approach that incorporates resolution kernels, which model the spatially-varying physical processes associated with photon emission, transport and detection. Our development is particularly suitable for applications where the projection data is sparse, such as high-resolution, dynamic, and time-of-flight PET reconstruction. The GPU approach runs more than 50 times faster than an equivalent CPU implementation while image quality and accuracy are virtually identical. This paper describes in details how the GPU can be used to accelerate the line projection operations, even when the lines-of-response have arbitrary endpoint locations and shift-varying resolution kernels are used. A quantitative evaluation is included to validate the correctness of this new approach.      

Hilbert transform based FBP algorithm for fan-beam CT full and partial scans

This paper presents a new type of filtered backprojection (FBP) algorithm for fan-beam full- and partial-scans. The filtering is shift-invariant with respect to the angular variable. The backprojection does not include position-dependent weights through the Hilbert transform and the one-dimensional transformation between the fan- and parallel-beam coordinates. The strong symmetry of the filtered projections directly leads to an exact reconstruction for partial data. The use of the Hilbert transform avoids the approximation introduced by the nonuniform cutoff frequency required in the ramp filter-based FBP algorithm. Variance analysis indicates that the algorithm might lead to a better uniformity of resolution and noise in the reconstructed image. Numerical simulations are provided to evaluate the algorithm with noise-free and noisy projections. Our simulation results indicate that the algorithm does have better stability over the ramp-filter-based FBP and circular harmonic reconstruction algorithms. This may help improve the image quality for in place computed tomography scanners with single-row detectors.     

Maximum entropy image reconstruction for an object with opaque obstructions

In the case of image reconstruction from missing projection data such as imaging an object with opaque obstructions, the conventional maximum entropy technique reconstructs a degraded image, which results from missing projection data. In this paper, we propose an improved maximum entropy technique based on a good estimation of missing projection data. Computer simulation using the proposed algorithm shows a significant improvement in image quality and convergence behavior over the conventional algorithms. This algorithm is also applied successfully to ultrasound attenuation CT (computed tomography) using a sponge phantom.     

Image reconstruction and enhanced resolution imaging from irregularsamples

While high resolution, regularly gridded observations are generally preferred in remote sensing, actual observations are often not evenly sampled and have lower-than-desired resolution. Hence, there is an interest in resolution enhancement and image reconstruction. This paper discusses a general theory and techniques for image reconstruction and creating enhanced resolution images from irregularly sampled data. Using irregular sampling theory, we consider how the frequency content in aperture function-attenuated sidelobes can be recovered from oversampled data using reconstruction techniques, thus taking advantage of the high frequency content of measurements made with nonideal aperture filters. We show that with minor modification, the algebraic reconstruction technique (ART) is functionally equivalent to Grochenig's (1992) irregular sampling reconstruction algorithm. Using simple Monte Carlo simulations, we compare and contrast the performance of additive ART, multiplicative ART, and the scatterometer image reconstruction (SIR) (a derivative of multiplicative ART) algorithms with and without noise. The reconstruction theory and techniques have applications with a variety of sensors and can enable enhanced resolution image production from many nonimaging sensors. The technique is illustrated with ERS-2 and SeaWinds scatterometer data     

Modeling and incorporation of system response functions in 3-D whole body PET

Appropriate application of spatially variant system models can correct for degraded resolution response and mispositioning errors. This paper explores the detector blurring component of the system model for a whole body positron emission tomography (PET) system and extends this factor into a more general system response function to account for other system effects including the influence of Fourier rebinning (FORE). We model the system response function as a three-dimensional (3-D) function that blurs in the radial and axial dimension and is spatially variant in radial location. This function is derived from Monte Carlo simulations and incorporates inter-crystal scatter, crystal penetration, and the blurring due to the FORE algorithm. The improved system model is applied in a modified ordered subsets expectation maximization (OSEM) algorithm to reconstruct images from rebinned, fully 3-D PET data. The proposed method effectively removes the spatial variance in the resolution response, as shown in simulations of point sources. Furthermore, simulation and measured studies show the proposed method improves quantitative accuracy with a reduction in tumor bias compared to conventional OSEM on the order of 10%-30% depending on tumor size and smoothing parameter.     

Performance characteristics of the 3-D OSEM algorithm in the reconstruction of small animal PET images. Ordered-subsets expectation-maximixation

Rat brain images acquired with a small animal positron emission tomography (PET) camera and reconstructed with the three-dimensional (3-D) ordered-subsets expectation-maximization (OSEM) algorithm with resolution recovery have better quality when the brain is imaged by itself than when inside the head with surrounding background activity. The purpose of this study was to characterize the dependence of this effect on the level of background activity, attenuation, and scatter. Monte Carlo simulations of the imaging system were performed. The coefficient of variation from replicate images, full-width at half-maximum (FWHM) from point sources and image profile fitting, and image contrast and uniformity were used to evaluate algorithm performance. A rat head with the typical levels of five and ten times the brain activity in the surrounding background requires additional iterations to achieve the same resolution as the brain-only case at a cost of 24% and 64% additional noise, respectively. For the same phantoms, object scatter reduced contrast by 3%-5%. However, attenuation degraded resolution by 0.2 mm and was responsible for up to 12% nonuniformity in the brain images suggesting that attenuation correction is useful. Given the effects of emission and attenuation distribution on both resolution and noise, simulations or phantom studies should be used for each imaging situation to select the appropriate number of OSEM iterations to achieve the desired resolution-noise levels.     

A maximum NEC criterion for Compton collimation to accurately identify true coincidences in PET

In this work, we propose a new method to increase the accuracy of identifying true coincidence events for positron emission tomography (PET). This approach requires 3-D detectors with the ability to position each photon interaction in multi-interaction photon events. When multiple interactions occur in the detector, the incident direction of the photon can be estimated using the Compton scatter kinematics (Compton Collimation). If the difference between the estimated incident direction of the photon relative to a second, coincident photon lies within a certain angular range around colinearity, the line of response between the two photons is identified as a true coincidence and used for image reconstruction. We present an algorithm for choosing the incident photon direction window threshold that maximizes the noise equivalent counts of the PET system. For simulated data, the direction window removed 56%-67% of random coincidences while retaining > 94% of true coincidences from image reconstruction as well as accurately extracted 70% of true coincidences from multiple coincidences.     

Tomographic microwave diversity image reconstruction employingunitary compression

Data compression through a unitary transform is utilized in tomographic microwave diversity image reconstruction in order to reduce the dimensionality and to extract the features in the data space. The unitary compression is derived by minimizing the mean-square error (MSE) and the unitary transform is made of eigenvectors of the data's covariance, regarded as a Karhunen-Loeve transform. Tomographic microwave frequency-swept imaging was developed using a unique target-derived reference technique to access the three dimensional Fourier space of the scatterer and an image reconstruction algorithm based on the projection slice theorem. It is shown that centimeter resolution of a complex object can be preserved even when half of the data set is compressed and that the reconstructed image remains identifiable by a human observer even when 2/3 of the data set is compressed     

Comparison of list-mode and DIRECT approaches for time-of-flight PET reconstruction

Early clinical results with time-of-flight (TOF) positron emission tomography (PET) systems have demonstrated the advantages of TOF information in PET reconstruction. Reconstruction approaches in TOF-PET systems include list-mode and binned iterative algorithms as well as confidence-weighted analytic methods. List-mode iterative TOF reconstruction retains the resolutions of the data in the spatial and temporal domains without any binning approximations but is computationally intensive. We have developed an approach [DIRECT (direct image reconstruction for TOF)] to speed up TOF-PET reconstruction that takes advantage of the reduced angular sampling requirement of TOF data by grouping list-mode data into a small number of azimuthal views and co-polar tilts and depositing the grouped events into histo-images, arrays with the sampling and geometry of the final image. All physical effects are included in the system model and deposited in the same histo-image structure. Using histo-images allows efficient computation during reconstruction without ray-tracing or interpolation operations. The DIRECT approach was compared with 3-D list-mode TOF ordered subsets expectation maximization (OSEM) reconstruction for phantom and patient data taken on the University of Pennsylvania research LaBr (3) TOF-PET scanner. The total processing and reconstruction time for these studies with DIRECT without attention to code optimization is approximately 25%-30% that of list-mode TOF-OSEM to achieve comparable image quality. Furthermore, the reconstruction time for DIRECT is independent of the number of events and/or sizes of the spatial and TOF kernels, while the time for list-mode TOF-OSEM increases with more events or larger kernels. The DIRECT approach is able to reproduce the image quality of list-mode iterative TOF reconstruction both qualitatively and quantitatively in measured data with a reduced time.     

Image reconstruction by conditional entropy maximisation for PET system

The authors show that the conditional entropy maximisation algorithm is a generalised version of the maximum likelihood algorithm for positron emission tomography (PET). Promising properties of the conditional entropy maximisation algorithm are as follows: an assumption is made that the entropy of the information content of the data should be maximised; it is a consistent way of selecting an image from the very many images that fit the measurement data; this approach takes care of the positivity of the reconstructed image pixels, since entropy does not exist for negative image pixel values; and inclusion of prior distribution knowledge in the reconstruction process is possible. Simulated experiments performed on a PET system have shown that the quality of the reconstructed image using the entropy maximisation method is good. A Gibbs distribution is used to incorporate prior knowledge into the reconstruction process. The mean squared error (MSE) of the reconstructed images shows a sharp new dip, confirming improved image reconstruction. The entropy maximisation method is an alternative approach to maximum likelihood (ML) and maximum a posteriori (MAP) methodologies.     

Aperture collimation correction and maximum-likelihood image reconstruction for near-field coded aperture imaging of single photon emission computerized tomography

Coded aperture (CA) imaging originally developed in X-ray astronomy has not been widely used in nuclear medicine due to the decoding complexity of near-field CA images. In this paper, we present a near-field CA imaging technique and image reconstruction method for high sensitivity and high resolution single photon emission computerized tomography (SPECT). Our approach makes three contributions. First, a correction method for the aperture collimation effect is used to eliminate the near-field artifacts without dual acquisitions of mask and anti-mask images. Second, a maximum-likelihood expectation-maximization (MLEM) deconvolution method is used to restore CA images. Finally, a new MLEM-based algorithm is used to partially reconstruct three-dimensional (3-D) objects from a single projection of CA images. Experiments conducted using a dual-head SPECT system equipped with a parallel-hole collimator and a CA module show a tenfold increase in count sensitivity and significant improvement in image resolution with CA collimation as compared to parallel-hole collimation. Experiments conducted using the same dual-head SPECT system equipped with a pinhole collimator show that when the object is closer to the pinhole collimator the CA image resolution is only slightly inferior to the pinhole collimated image. We found that the MLEM deconvolution method provides an inherent nonnegativity constraint on pixel values and remarkably reduces background activities of CA images. The MLEM reconstruction algorithm for CA images is capable of reconstructing 3-D objects from a single projection and can be potentially extended to full 3-D SPECT reconstruction for CA images.     

一种多目标优化重建方法在气体浓度层析成像中的应用

为了克服传统的少射线图像重建方法-ART对噪声敏感而导致的重建图像质量差的问题,在考虑气体扩散时其浓度二维分布特点的基础上,提出了一种利用多目标优化的方法来重建气体二维浓度分布图的方法.实验表明,该算法对改善气体浓度层析成像中的噪声对重建结果的影响具有较好的效果.     

A Super-Resolution Framework for 3-D High-Resolution and High-Contrast Imaging Using 2-D Multislice MRI

A novel super-resolution reconstruction (SRR) framework in magnetic resonance imaging (MRI) is proposed. Its purpose is to produce images of both high resolution and high contrast desirable for image-guided minimally invasive brain surgery. The input data are multiple 2-D multislice inversion recovery MRI scans acquired at orientations with regular angular spacing rotated around a common frequency encoding axis. The output is a 3-D volume of isotropic high resolution. The inversion process resembles a localized projection reconstruction problem. Iterative algorithms for reconstruction are based on the projection onto convex sets (POCS) formalism. Results demonstrate resolution enhancement in simulated phantom studies, and ex vivo and in vivo human brain scans, carried out on clinical scanners. A comparison with previously published SRR methods shows favorable characteristics in the proposed approach.