I. K. Hong

A fusion PET-MRI system with a high-resolution research tomograph-PET and ultra-high field 7.0 T-MRI for the molecular-genetic imaging of the brain.

We have developed a positron emission tomography (PET) and magnetic resonance imaging (MRI) fusion system for the molecular‐genetic imaging (MGI) of the in vivo human brain using two high‐end imaging devices: the HRRT‐PET, a high‐resolution research tomograph dedicated to brain imaging on the molecular level, and the 7.0 T‐MRI, an ultra‐high field version used for morphological imaging. HRRT‐PET delivers high‐resolution molecular imaging with a resolution down to 2.5 mm full width at half maximum (FWHM), which allows us to observe the brains molecular changes using the specific reporter genes and probes. On the other front, the 7.0 T‐MRI, with submillimeter resolution images of the cortical areas down to 250 μm, allows us to visualize the fine details of the brainstem areas as well as the many cortical and subcortical areas. The new PET–MRI fusion imaging system will provide many answers to the questions on neurological diseases as well as cognitive neurosciences. Some examples of the answers are the quantitative visualization of neuronal functions by clear molecular and genetic bases, as well as diagnoses of many neurological diseases such as Parkinsons and Alzheimers. The salient point of molecular‐genetic imaging and diagnosis is the fact that they precede the morphological manifestations, and hence, the early and specific diagnosis of certain diseases, such as cancers.

Image based resolution modeling for the HRRT OSEM reconstructions software

The implementation and the measurement of an approximate image based model of the ECAT HRRT PET scanner response function, designed for its regular OSEM reconstruction software, are presented. The system matrix used in the iterative reconstruction is factorized into two terms: first a matrix modeling the blurring effects in the image space, followed by the projection matrix. The methodology used to measure the elements of the image based blurring matrix is presented and applied to three HRRT scanners. A spatially invariant resolution model was chosen; the columns of the blurring matrix are then defined as shifted copies of a stationary blurring kernel. This kernel was modeled as the sum of two isotropic 3D Gaussian functions. The results of the resolution measurement varied between the three scanners: at the center of the field-of-view, the standard deviation varied between 0.85 and 1.00 mm for the first Gaussian and between 2.0 and 2.7 mm for the second Gaussian. The ratio between the second and the first Gaussians was 0.07.

Ultra fast 4D PET image reconstruction with user-definable temporal basis functions

Fully 4D image reconstruction, through its use of temporally extensive basis functions, is able to reduce spatiotemporal noise in dynamic PET imaging. This noise reduction has the potential to benefit post-reconstruction kinetic analysis, resulting in improved parametric images. However these benefits come at a significant computational cost: fully 4D reconstruction requires access to the entire time series of fully 3D sinograms (along with the same number of fully 3D scatter and randoms sinogram estimates) in the innermost iterative reconstruction loop. This results in a huge in-memory storage requirement combined with a projection/backprojection workload in the innermost reconstruction loop which is up to 10–40 times greater than conventional static 3D reconstruction (depending on the number of frames). This work presents a practical 4D methodology which i) uses an extremely efficient symmetry & SIMD forward and backprojector for ultra fast computation, ii) compresses the time series of dynamic sinogram data sets without information loss, and iii) permits the use of any user-specified set of temporal basis functions. The result is an extremely fast and flexible fully 4D iterative reconstruction methodology, greatly facilitating the determination of the (perhaps study-specific) optimal temporal basis functions. Whereas single CPU processing for fully 4D list-mode data reconstruction can take in excess of 2 weeks on a single node, the proposed method (using two quad-core CPUs, with span 9 projection data) takes approximately 3.5 hours, giving close to two orders of magnitude acceleration. The method is demonstrated on measured HRRT (High Resolution Research Tomograph) PET data for a [18F]flumazenil study and for an [18F]MPPF study.

Fast forward projection and backward projection algorithm using SIMD

Recent developments in PET scanners such as the HRRT (High Resolution Research Tomograph) developed by Siemens greatly enhanced their resolution as well as sensitivity, but they increased coincidence lines of response more than 4.5 times 10 generated by as many nuclear detectors as 120,000. This formidable amount of data poses a real problem in the image reconstruction and its applications. It also has been the major bottleneck in further developments of the higher resolution PET scanners. To remedy this problem in the image reconstruction, we developed a new algorithm based on the SIMD (Single Instruction Multiple Data) technique incorporated with the symmetry properties of the projection and backprojection processes, especially in the 3D OSEM algorithm. We refer to this technique as the SSP (Symmetry and SIMD based Projection-backprojection) algorithm. As a demonstration, the algorithm was applied to the OSEM (Ordered Subset Expectation Maximization) 3D algorithm with HRRT data and it effectively reduced the total image reconstruction time to 80 folds.

On algorithms for minimum-cost quickest paths with multiple delay-bounds

The quickest path problem deals with the transmission of a message of size σ from a source to a destination with the minimum end-to-end delay over a network with bandwidth and delay constraints on the links. We adapt properties of the quickest path to solve the delay-bounded minimum-cost (DBMC) path problem that is known to be the NP-hard. In this paper, we propose two efficient and simple algorithms, DBMCQP and DBMCQRT. DBMCQP computes a DBMC quickest path for a given message size σ with O(rm + rnlogn), and DBMCQRT construct DBMC routing tables taking into account multiple delay-bounds for any size of message with O(kr2), where r, n, m, and k are the number of distinct link-bandwidths, nodes, links of the network, and the number of delay-bounds, respectively.

Ultrafast Preconditioned Conjugate Gradient OSEM algorithm for fully 3D PET reconstruction

The Conjugate Gradient (CG) method is an optimization algorithm used to determine the numerical solution of particular systems of linear equations which may be expressed as a symmetric and positive definite matrix. The CG method is iterative, so it can be applied to systems which are too large to be handled by direct methods. The CG method can also be used to solve unconstrained optimization problems such as PET reconstruction. In the Bayesian PET reconstruction problem, Preconditioned Conjugate Gradient (PCG) algorithms were previously shown to have more favorable convergence rates than expectation maximization (EM) type algorithms [1]. However, PCG fails to converge on partial datasets. Block iterative methods such as Ordered Subset Expectation Maximization (OSEM) have become the most commonly used methods in PET reconstruction, as they require less iteration than PCG. This work combines both algorithms, PCG-OSEM, to reduce the number of iterations and speed up the convergence of OSEM. The proposed search direction of the CG is orthogonal to previous search directions, and in the image space rather than projection domain. Therefore, single iteration can be performed to achieve an acceptable PET reconstructed image.

Ultra Fast Frame Based Parallel Reconstruction (FBPR) for dynamic 3D PET study

Dynamic study using positron emission tomography (PET) is a powerful tool to analyze neurochemical and neuropharmachological processes in vivo. However, full-reconstruction (including histogramming, precorrections, and reconstruction) for dynamic PET studies is a very time-consuming task, especially with PET scanners of high resolution and high sensitivity, such as HRRT (high resolution research tomograph) developed by Siemens/CTI. For example, the full-reconstruction time for the dynamic study of 32 frames using HRRT takes above 21 hours. To solve this excessive computational time problem, we have developed the ultra fast frame based parallel reconstruction (FBPR) system by effectively expanding the symmetry and SIMD based projection-backprojection (SSP) algorithm[1] into a cluster system. In contrast to conventional cluster system approaches, the FBPR system uses the frame as the granularity of parallelization for dynamic study reconstruction, and simultaneously reconstructs maximum frame images same as the number of computing nodes. We applied the FBPR system into HRRT and tested the performance of the system. Compared with the existing cluster reconstruction system, the FBPR system enhanced the performance by up to twenty five times and also provided the same quality reconstructed images.

Ultrafast Preconditioned Conjugate Gradient MAP reconstruction for fully 3-D microPET

Iterative 3D PET reconstruction represents a very computational challenge due to the large number of lines of response (LOR) collected for each data set. This iterative 3D reconstruction also needs a lot of iterations to achieve an acceptable PET reconstructed image. A Preconditioned Conjugate Gradient (PCG) method was previously shown to have faster convergence rate than expectation maximization (EM) type algorithms. For the microPET, imagea suffer from crystal penetration blurring due to small scanner radius. An exact 2D blur model is needed to achieve high resolution image. A Preconditioned Conjugate Gradient (PCG) method is described for reconstruction of high-resolution 3D images from the microPET Inveon small-animal scanner from Siemens [1, 2, 3]. The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, attenuation correction, and detector efficiency corrections. The system matrix for geometric projection is based on depth dependent solid angle calculation in combination with a spatially variant detector response model. The mircoPET PCG is combined with OSEM to accelerate convergence. This reconstruction model achieves a high resolution animal image; however, it took an hour to reconstruct a frame. Therefore, we describe an ultrafast forward and back projector pair based on Symmetry and SIMD projector (SSP) [4]. The proposed method produces similar quality images when compared to those obtained with the software package from Siemens and requires order of magnitude less computation.

Fast 3-D motion correction using the characteristics of motion in rigid body

The proposed method introduced in this study is to achieve fast the motion correction that the computation costs of the process had been a burden of implementation of motion compensation. With pre-determinable ranges of rotation angles of φ and θ, and the motion transformation matrix that can be calculated at preprocessing stage before executing image reconstruction algorithm, motion correction can be performed fast. In addition, with the reduction of the computational cost shown in this study, motion correction is achieved in sinogram domain. This method is also beneficial to use of iterative expectation maximization reconstruction algorithms since a motion corrected sensitivity image can be generated with reduced computations.

New concurrent acquisition and reconstruction (CAR) system for PET study

PET has been advanced more than 30 years and finally, high spatial resolution PET having FWHM resolution of 2.5 mm, such as HRRT, has been developed. However, excessive reconstruction time still left as a major problem. This can be more serious at HRRT system which processes huge amount of data acquired from more than 120,000 detectors. For example, it takes about 80 minutes to reconstruct a single frame image at the HRRT system even with the eight-node cluster reconstruction system provided by Siemens. Due to this very long reconstruction time, it has been impossible in the PET studies to conduct real-time reconstruction or concurrent reconstruction while scanning. We developed a new concurrent acquisition and reconstruction (CAR) system by extending the FBPR system and the SSP algorithm. With the CAR system, the operator can immediately check the scanning status by observing the fully reconstructed image of each frame while scanning. So, the operator can interactively control the intensity at a specific ROI by checking the reconstructed image and managing dose activity while PET scan. The CAR system firstly makes the real-time reconstruction possible and provides numerous new opportunities to the neuroscience studies. In fact, we combined the CAR system and HRRT and conducted real time reconstruction for 32 frames dynamic study. In addition, the new system can be used as the high-speed reconstruction system for the dynamic PET scan reconstruction. When the scan is finished, the CAR system provides all the frame images within the time required only for a final single frame reconstruction.