Sanghee Cho

Exact and approximate Fourier rebinning of PET data from time-of-flight to non time-of-flight

The image reconstruction problem for fully 3D TOF PET is challenging because of the large data sizes involved. One approach to this problem is to first rebin the data into one of the following lower dimensional formats: 2D TOF, 3D non TOF or 2D non TOF. Here we present a unified framework based on a generalized projection slice theorem for TOF data that can be used to compute each of these mappings. We use this framework to develop approaches for rebinning into non TOF formats without significant loss of information. We first derive the exact mappings and then describe approximations which address the missing data problem for oblique sinograms. We evaluate the performance of approximate rebinning using Monte Carlo simulations. Our results show that rebinning into non TOF sinograms retains significant SNR advantages over sinograms collected without TOF information.

Iterative Image Reconstruction Using Inverse Fourier Rebinning for Fully 3-D PET

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully 3-D positron emission tomography (PET). 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, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a 2-D projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing lines of response (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation

Optimal Rebinning of Time-of-Flight PET Data

Time-of-flight (TOF) positron emission tomography (PET) scanners offer the potential for significantly improved signal-to-noise ratio (SNR) and lesion detectability in clinical PET. However, fully 3D TOF PET image reconstruction is a challenging task due to the huge data size. One solution to this problem is to rebin TOF data into a lower dimensional format. We have recently developed Fourier rebinning methods for mapping TOF data into non-TOF formats that retain substantial SNR advantages relative to sinograms acquired without TOF information. However, mappings for rebinning into non-TOF formats are not unique and optimization of rebinning methods has not been widely investigated. In this paper we address the question of optimal rebinning in order to make full use of TOF information. We focus on FORET-3D, which approximately rebins 3D TOF data into 3D non-TOF sinogram formats without requiring a Fourier transform in the axial direction. We optimize the weighting for FORET-3D to minimize the variance, resulting in H2-weighted FORET-3D, which turns out to be the best linear unbiased estimator (BLUE) under reasonable approximations and furthermore the uniformly minimum variance unbiased (UMVU) estimator under Gaussian noise assumptions. This implies that any information loss due to optimal rebinning is as a result only of the approximations used in deriving the rebinning equation and developing the optimal weighting. We demonstrate using simulated and real phantom TOF data that the optimal rebinning method achieves variance reduction and contrast recovery improvement compared to nonoptimized rebinning weightings. In our preliminary study using a simplified simulation setup, the performance of the optimal rebinning method was comparable to that of fully 3D TOF MAP.

Monte Carlo based estimation of detector response in a large solid angle Preclinical PET imaging system

Small animal PET imaging imposes high performance requirements on image resolution and system sensitivity. Scanners with larger solid angle, achieved by using smaller crystal ring diameter and longer axial field-of-view (FOV), have higher absolute sensitivity. The Inveon dedicated PET (DPET) system, the latest generation of commercial tomographs from Siemens Preclinical Solutions, Inc., is such a high sensitivity scanner. Its crystal ring diameter and axial extent is 16.1 cm and 12.7 cm respectively, which give a solid angle coverage of 62%. However, this geometry also accentuates inter-crystal penetration, especially in the axial direction and causes axial blurring. Axial and radial blurring recovery is crucial for high resolution small animal PET imaging. System response modeling in combination with iterative reconstruction algorithms like Maximum a posteriori reconstruction (MAP) can be used to recover the resolution loss. Blurring in both radial and axial directions were simulated in GATE with a planar strip of 18F source placed inside the Inveon scanner. Detector response for each possible line of response (LOR) was calculated and can be incorporated into iterative reconstruction algorithms. As the entrance ring difference (δ) increased, the recorded coincidences tended to shift to a larger ring difference. As the entrance radial offset (u) increased, the recorded coincidences tended to shift to a smaller radial offset. The blurring effect got larger as δ and/or u increased. A real 18F plane source printed on carbon paper was also imaged and compared with the simulation data as a validation. The coincidence counts recorded for each ring difference showed a very good agreement between simulation and experiment except for very large oblique angles. This discrepancy should be improved with the inclusion of the scanner end shields in future simulations.

Estimation of gap data using bow-tie filters for 3D time-of-flight PET

In many PET scanners, there exist gaps between detector blocks and the data corresponding to lines of response associated with these gaps are missing. The missing gap data must be estimated prior to image reconstruction in cases where the sinogram data are rebinned into lower dimensional formats or when filtered backprojection (FBP) is used. Both bilinear interpolation and filters enforcing data consistency conditions have been used for non-TOF PET data. Here we develop a method for gap filling for TOF data by iteratively applying a bow-tie filter in the Fourier domain. We use a Fourier rebinning method (FORET-2D) to rebin the 3D TOF PET data to 2D non-TOF data and then apply bow-tie filtering to each of the stacked 2D sinograms. The estimated gap data are extracted from the 3D TOF sinograms computed by inverse rebinning from the bow-tie filtered 2D non-TOF data. The procedure can be repeated iteratively to further refine the gap estimates. Preliminary results indicate that the new method provides improved estimates of the gap data compared to bilinear interpolation and reduces artifacts due to interpolation error.

Optimized weighting for Fourier rebinning of three-dimensional time-of-Flight PET data to non-time-of-flight

Time-of-flight (TOF) PET scanners provide the potential for significantly improved signal-to-noise ratio (SNR) and lesion detectability in clinical PET. Therefore, it is likely that TOF will become the standard for clinical whole body PET in the near future. However, fully 3D TOF PET image reconstruction is a challenging task due to the huge data size. One solution to this problem is to rebin TOF data into a lower dimensional format. We have recently developed Fourier rebinning methods for mapping TOF data into non-TOF formats and achieved substantial SNR advantages over sinograms acquired without TOF information. However, such mappings for rebinning into non-TOF formats are not unique and optimization of rebinning methods has not been widely investigated. In this paper we address the question of optimal rebinning in order to make full use of TOF information and consequently to maximize image quality. We focus on FORET-3D, which rebins 3D TOF data into 3D non-TOF sinogram formats without requiring a Fourier transform in the axial direction. We optimize the weighting for FORET-3D using a uniformly minimum variance unbiased (UMVU) estimator under reasonable approximations. We show that the rebinned data with optimal weights are a sufficient statistic for the unknown image, implying that any information loss due to rebinning is as a result only of the approximations used in developing the optimal weighting. We demonstrate using simulated and real phantom TOF data that the optimal rebinning method achieves significant variance reduction and better contrast recovery compared to other rebinning weightings.

Comparison of count rate sensitivity performance for a LSO-TOF system with a Cherenkov radiation based PbF 2 -TOF system

The use of Cherenkov light production and timing for TOF PET has been suggested, and there are papers indicating the possibility to improve timing in this way. The present paper, however, focuses only on count rate sensitivity issues by comparing a LSO-LSO system against a potential PbF2 system. This has been accomplished by using a simple two detector set up first looking at LSO-LSO coincidences and then exchanging the LSO crystal on one of the channels with PbF2 and then extracting the coincidence sensitivity for a pure PbF2 system. A simple comparison between the resulting LSO-LSO coincidence count rate and the PbF2-PbF2 coincidence count rate shows more than a 10 to 1 difference. In addition we have evaluated the time resolution achievable with two different photo sensor combinations, PMT-PMT and PMT-SiPM. Even if a time resolution of 50 ps may be possible to achieve in a PbF2 system, this requires very special photo sensors. Our results with standard photo sensors indicate time resolutions of the order of ~250 ps. If a 50 ps time resolution can be achieved, this may be equivalent to a 500 ps LSO system with 10 times higher sensitivity. One must consider, however, the minimum number of counts needed in a 50 ps system to achieve reasonable image quality. In addition to use very fast, photo sensors, these have to have high quantum efficiency from 250 nm up to 600 nm. Possible photo sensors for Cherenkov PET may be MCP PMTs.