A new virtual ring-based system matrix generator for iterative image reconstruction in high resolution small volume PET systems

Abstract

A common approach to improving the spatial resolution of small animal PET scanners is to reduce the size of scintillation crystals and/or employ high resolution pixellated semiconductor detectors. The large number of detector elements results in the system matrix-an essential part of statistical iterative reconstruction algorithms-becoming impractically large. In this paper, we propose a methodology for system matrix modelling which utilises a virtual single-layer detector ring to greatly reduce the size of the system matrix without sacrificing precision. Two methods for populating the system matrix are compared; the first utilises a geometrically-derived system matrix based on Siddon's ray tracer method with the addition of an accurate detector response function, while the second uses Monte Carlo simulation to populate the system matrix. The effectiveness of both variations of the proposed technique is demonstrated via simulations of PETiPIX, an ultra high spatial resolution small animal PET scanner featuring high-resolution DoI capabilities, which has previously been simulated and characterised using classical image reconstruction methods. Compression factors of × 5 10 7 and × 2.5 10 7 are achieved using this methodology for the system matrices produced using the Institute of Physics and Engineering in MedicineContent from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. geometric and Monte Carlo-based approaches, respectively, requiring a total of 0.5-1.2 GB of memory-resident storage. Images reconstructed from Monte Carlo simulations of various point source and phantom models, produced using system matrices generated via both geometric and simulation methods, are used to evaluate the quality of the resulting system matrix in terms of achievable spatial resolution and the CRC, CoV and CW-SSIM index image quality metrics. The Monte Carlo-based system matrix is shown to provide the best image quality at the cost of substantial one-off computational effort and a lower (but still practical) compression factor. Finally, a straightforward extension of the virtual ring method to a three dimensional virtual cylinder is demonstrated using a 3D DoI PET scanner.

Recent advances in combined Positron Emission Tomography and Magnetic Resonance Imaging

“…SRMs have been estimated using either analytical, experimental, MC, or hybrid approaches. Analytical approaches are based on geometrical projection models [54,[178][179][180][181], analytical models of the physical processes [182][183][184][185], or convolutional kernels usually referred to as Point Spread Function (PSF) [186]. The PSF is a widely used method for SRM modeling [187], consisting of either image or projection blurring kernels applied as a convolution operation.…”

“…Since these matrices require high loads of memory storage, symmetries and SRM sparsity have been exploited to reduce the SRM size. Some authors applied PSF descriptions [185,[204][205][206][207], or wide tubes-of-response (TORs) [208][209][210][211] instead of simple projection models. Other approaches include separate positron range correction, which is included in the reconstruction as an image blurring kernel [212,213].…”

Towards quantitative small-animal imaging on hybrid PET/CT and PET/MRI systems

“…Recently, a general algorithm called symmetry search algorithm was proposed to automatically depict the geometrical symmetries in various scanners, leading to higher compression factors compared to conventional methods [83]. One of the most distinctive approaches to compress the prohibitive size of the SRM with multi-layered crystals with DOI capability was suggested by Li et al, in which the DOI information from all layers was summarized in a smaller virtual ring around the object, leading to a drastic reduction in SRM dimension by a factor of 2 × 10 7 [84].…”

Estimation of optimized timely system matrix with improved image quality in iterative reconstruction algorithm: A simulation study

“…The system matrix (SM) indicating relationship between the object and projection space is a main part of statistical image reconstruction algorithms. It is calculated by three methods as; (i) analytical method in which the common regions (CR) considering as interacting probability of emitted gamma photons with detector elements are calculated by geometrical relations [17,18,19,20,21]; (ii) Monte Carlo (MC) simulations by modeling a digital phantom and estimating projections, which the ratio of counts in i-th element of detector for the originated photons from j-th pixel of object matrix is considered as a i,j element of the SM [22,23,24]; and (iii) experimental method where the SM is obtained by measuring projections around the phantoms [25,26].…”