Vladimir Y. Panin

Fully 3-D PET reconstruction with system matrix derived from point source measurements

The quality of images reconstructed by statistical iterative methods depends on an accurate model of the relationship between image space and projection space through the system matrix. The elements of the system matrix for the clinical Hi-Rez scanner were derived by processing the data measured for a point source at different positions in a portion of the field of view. These measured data included axial compression and azimuthal interleaving of adjacent projections. Measured data were corrected for crystal and geometrical efficiency. Then, a whole system matrix was derived by processing the responses in projection space. Such responses included both geometrical and detection physics components of the system matrix. The response was parameterized to correct for point source location and to smooth for projection noise. The model also accounts for axial compression (span) used on the scanner. The forward projector for iterative reconstruction was constructed using the estimated response parameters. This paper extends our previous work to fully three-dimensional. Experimental data were used to compare images reconstructed by the standard iterative reconstruction software and the one modeling the response function. The results showed that the modeling of the response function improves both spatial resolution and noise properties

An Assessment of the Impact of Incorporating Time-of-Flight Information into Clinical PET/CT Imaging

The introduction of fast scintillators with good stopping power for 511-keV photons has renewed interest in time-of-flight (TOF) PET. The ability to measure the difference between the arrival times of a pair of photons originating from positron annihilation improves the image signal-to-noise ratio (SNR). The level of improvement depends upon the extent and distribution of the positron activity and the time resolution of the PET scanner. While specific estimates can be made for phantom imaging, the impact of TOF PET is more difficult to quantify in clinical situations. The results presented here quantify the benefit of TOF in a challenging phantom experiment and then assess both qualitatively and quantitatively the impact of incorporating TOF information into the reconstruction of clinical studies. A clear correlation between patient body mass index and gain in SNR was observed in this study involving 100 oncology patient studies, with a gain due to TOF ranging from 1.1 to 1.8, which is consistent with the 590-ps time resolution of the TOF PET scanner. The visual comparison of TOF and non-TOF images performed by two nuclear medicine physicians confirmed the advantages of incorporating TOF into the reconstruction, advantages that include better definition of small lesions and image details, improved uniformity, and noise reduction.

First experimental results of time-of-flight reconstruction on an LSO PET scanner

Time-of-flight (TOF) positron emission tomography (PET) was studied and preliminarily developed in the 1980s, but the lack of a scintillator able to deliver at the same time proper time resolution and stopping power has prevented this technique from becoming widespread and commercially available. With the introduction of LSO in PET, TOF is now a feasible option. TOF reconstruction has been implemented in the CPS Hi-Rez PET scanner, both with 2D filtered-back-projection (FBP2D) and 3D ordered subset expectation maximization (OSEM3D). A new procedure has been introduced in the time alignment to compensate for the limited digital time resolution of the present electronics. A preliminary version of scatter correction for TOF has been devised and is presented. The measured time resolution of 1.2 ns (FWHM) allowed for a signal-to-noise ratio increase of about 50% in phantoms of about 40 cm transaxial size, or a gain larger than 2 in noise equivalent counts (NEC). TOF reconstruction has shown the expected improvement in SNR, both in simulation and experimental data. First experimental results show two improvements of TOF reconstruction over conventional (non-TOF) reconstruction: a lower noise level and a better capability to resolve structures deep inside large objects.

Total variation regulated EM algorithm [SPECT reconstruction]

An iterative Bayesian reconstruction algorithm based on the total variation (TV) norm constraint is proposed. The motivation for using TV regularization is that it is extremely effective for recovering edges of images. This paper extends the TV norm minimization constraint to the field of SPECT image reconstruction with a Poisson noise model. The regularization norm is included in the OSL-EM (one step late expectation maximization) algorithm. Unlike many other edge-preserving regularization techniques, the TV based method depends one parameter. Reconstructions of computer simulations and patient data show that the proposed algorithm has the capacity to smooth noise and maintain sharp edges without introducing over/under shoots and ripples around the edges.

Total variation regulated EM algorithm

An iterative Bayesian reconstruction algorithm based on the total variation (TV) norm constraint is proposed. The motivation for using TV regularization is that it is extremely effective for recovering edges of images. The TV norm minimization, introduced in 1992 was shown to be effective for restoring blurred images with a Gaussian noise model and was demonstrated to be effective for noise suppression and edge preservation. The images were diffused according to a set of nonlinear anisotropic diffusion partial differential equations, which suffered from computational difficulties. This paper extends the TV norm minimization constraint to the field of SPECT image reconstruction with a Poisson noise model. The regularization norm is included in the ML-EM (maximum likelihood expectation maximization) algorithm. The partial differential equation approach is not utilized here. Reconstructions of computer simulations and patient data show that the proposed algorithm has the capacity to smooth the noise and maintain sharp edges without introducing over/under shoots and ripples around the edges.

PET reconstruction with system matrix derived from point source measurements

The quality of images reconstructed by statistical iterative methods depends on an accurate model of the relationship between image space and projection space through the system matrix. A method of acquiring the system matrix on the CPS Innovations the HiRez scanner was developed. The system matrix was derived by positioning the point source in the scanner field of view and processing the response in projection space. Such responses include geometrical and detection physics components of the system matrix. The response is parameterized to correct point source location and to smooth projection noise. Special attention was paid to span concepts of HiRez scanner. The projection operator for iterative reconstruction was constructed, taking into account estimated response parameters. The computer generated and acquired data were used to compare reconstruction obtained by the HiRez standard software and produced by better modeling. Results showed that the better resolution and noise property can be achieved.

Variance reduction on randoms from coincidence histograms for the HRRT

A new algorithm for variance reduction on random coincidences (VRR) has been validated for the HRRT. VRR is crucial to achieve quantitation for low statistics dynamic studies reconstructed with iterative methods based on ordinary Poisson model. On HRRT, VRR cannot be performed in projection space since individual LORs are mixed after histogramming in parallel projection space using nearest neighbor approximation and axial compression. The proposed algorithm uses the classical random rate equation on the 4.5 109LORs. However, crystal singles are registered at block level and have lower deadtime than coincidences. Variations in layer identification with countrate were reported biasing random estimation from block singles. Our method overcomes these problems by estimating the singles per crystal from delayed coincidences. A singles map is created histogramming every delayed event into 2 singles. Each element represents the number of coincidences between that crystal and the ones in the 5 opposite coincident heads. The algorithm finds iteratively the crystal singles rates compatible with the delayed coincidence events. The method has been validated on decaying phantoms. We compared estimated and measured block singles to identify deadtime difference between singles and coincidences

Continuous and Discrete Data Rebinning in Time-of-Flight PET

This paper investigates data compression methods for time-of-flight (TOF) positron emission tomography (PET), which rebin the 3-D TOF measurements into a set of 2-D TOF data for a stack of transaxial slices. The goal of this work is to develop re- binning algorithms that are more accurate than the TOF single- slice-rebinning (TOF-SSRB) method proposed by Mullani in 1982. Two approaches are explored. The first one is based on a partial differential equation, which expresses a consistency condition for TOF-PET data with a Gaussian TOF profile. From this equation we derive an analytical rebinning algorithm, which is unbiased in the limit of continuous sampling. The second approach is discrete: each 2-D rebinned data sample is calculated as a linear combination of the 3-D TOF samples in the same axial plane parallel to the axis of the scanner. The coefficients of the linear combination are precomputed by optimizing a cost function which enforces both accuracy and good variance reduction, models the TOF profile, the axial PSF of the LORs, and the specific sampling scheme of the scanner. Measurements of a thorax phantom on a prototype TOF-PET scanner with a resolution of 550 ps show that the proposed discrete method improves the bias-variance trade-off and is a promising alternative to TOF-SSRB when data compression is required to achieve clinically acceptable reconstruction time.

Simultaneous reconstruction of emission activity and attenuation coefficient distribution from TOF data, acquired with external transmission source

The simultaneous PET data reconstruction of emission activity and attenuation coefficient distribution is presented, where the attenuation image is constrained by exploiting an external transmission source. Data are acquired in time-of-flight (TOF) mode, allowing in principle for separation of emission and transmission data. Nevertheless, here all data are reconstructed at once, eliminating the need to trace the position of the transmission source in sinogram space. Contamination of emission data by the transmission source and vice versa is naturally modeled. Attenuated emission activity data also provide additional information about object attenuation coefficient values. The algorithm alternates between attenuation and emission activity image updates. We also proposed a method of estimation of spatial scatter distribution from the transmission source by incorporating knowledge about the expected range of attenuation map values. The reconstruction of experimental data from the Siemens mCT scanner suggests that simultaneous reconstruction improves attenuation map image quality, as compared to when data are separated. In the presented example, the attenuation map image noise was reduced and non-uniformity artifacts that occurred due to scatter estimation were suppressed. On the other hand, the use of transmission data stabilizes attenuation coefficient distribution reconstruction from TOF emission data alone. The example of improving emission images by refining a CT-based patient attenuation map is presented, revealing potential benefits of simultaneous CT and PET data reconstruction.

LSO background radiation as a transmission source using time of flight.

LSO scintillators (Lu2Sio5:Ce) have a background radiation which originates from the isotope Lu-176 that is present in natural occurring lutetium. The decay that occurs in this isotope is a beta decay that is in coincidence with cascade gamma emissions with energies of 307, 202 and 88 keV. The coincidental nature of the beta decay with the gamma emissions allow for separation of the emission data originating from a positron annihilation event from transmission type data from the Lu-176 beta decay. By using the time of flight information, and information of the chord length between two LSO pixels in coincidence as a result of a beta emission and emitted gamma, a second time window can be set to observe transmission events simultaneously to emission events. Using the time when the PET scanner is not actively acquiring positron emission data, a continuous blank can be acquired and used to reconstruct a transmission image. With this blank and the measured transmission data, a transmission image can be reconstructed. This reconstructed transmission image can be used to perform emission data corrections such as attenuation correction and scatter corrections. It is observed that the flux of the background activity is high enough to create good transmission images with an acquisition time of 10 minutes.