MAP reconstruction for Fourier rebinned TOF-PET data

Abstract

Time-of-flight (TOF) information improves signal to noise ratio in Positron Emission Tomography (PET). Computation cost in processing TOF-PET sinograms is substantially higher than for nonTOF data because the data in each line of response is divided among multiple time of flight bins. This additional cost has motivated research into methods for rebinning TOF data into lower dimensional representations that exploit redundancies inherent in TOF data. We have previously developed approximate Fourier methods that rebin TOF data into either 3D nonTOF or 2D nonTOF formats. We refer to these methods respectively as FORET-3D and FORET-2D. Here we describe maximum a posteriori (MAP) estimators for use with FORET rebinned data. We first derive approximate expressions for the variance of the rebinned data. We then use these results to rescale the data so that the variance and mean are approximately equal allowing us to use the Poisson likelihood model for MAP reconstruction. MAP reconstruction from these rebinned data uses a system matrix in which the detector response model accounts for the effects of rebinning. Using these methods we compare performance of FORET-2D and 3D with TOF and nonTOF reconstructions using phantom and clinical data. Our phantom results show a small loss in contrast recovery at matched noise levels using FORET compared to reconstruction from the original TOF data. Clinical examples show FORET images that are qualitatively similar to those obtained from the original TOF-PET data but a small increase in variance at matched resolution. Reconstruction time is reduced by a factor of 5 and 30 using FORET3D+MAP and FORET2D+MAP respectively compared to 3D TOF MAP, which makes these methods attractive for clinical applications.

Optimization-Based Image Reconstruction From Low-Count, List-Mode TOF-PET Data

“…Algorithms based upon update procedures of the maximum-likelihood (ML)-expectation-maximization (EM) [1]–[5], maximum a posterior (MAP) [6]–[9], and penalized maximum likelihood (PML) methods [10]–[12], especially in an order-subset (OS) form [13]–[18], have been investigated and developed for reconstructing images of pre-clinical and clinical utility from time-of-flight (TOF) positron emission tomography (PET) [19]–[21]. However, some of the algorithms may also yield images of limited axial volume coverage (AVC) and of considerably deteriorating quality when applied to data of low counts [22], [23], which are often of application interests in performing fast and/or low-dose TOF-PET imaging.…”

Theory and realization of a 2D high resolution and high sensitivity SPECT system with an angle-encoding attenuator pattern

“…The increased calculation time caused by slow convergence using the new system is also an important factor that needs to be addressed in the future. Additional constraints such as boundary information could be added by using Maximum a posterior (MAP) (Bai et al 2014) approach for faster determination of boundary and background information in the early convergence stage. The update equation (10) could also be optimized by inverting measurement matrix M before reconstruction for faster convergence speed.…”

A unified Fourier theory for time-of-flight PET data

“…As for (30), both the approximate and exact implementations of Fourier rebinning for 3D non-TOF PET were given in Defrise et al (1997) and Liu et al (1999); the corresponding inverse rebinning for 3D non-TOF PET was given in Cho et al (2007). The approximate implementation of (20) to rebin 3D TOF-PET to 3D non-TOF PET data was implemented elsewhere (Cho et al 2009, Ahn et al 2011, Bai et al 2014. The exact rebinning of 3D TOF-PET data to 2D TOF-PET data using the consistency equation ( 17) was given in Defrise et al (2008).…”