Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

Abstract

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Projector model for efficient list-mode reconstruction in PET scanners with parallel planar detectors

“…Reconstructed data have been compared with histogram-mode 3D-OSEM [18] with precalculated system-matrix using Monte Cario methods and listmode OSEM with symmetric Gaussian model [17]. Direct (i.e., unregularized), and Median Root Prior (MRP) regularized versions [19] of the reconstruction algorithms were used.…”

Free Software for PET Imaging

“…In spite of being sparse in nature, the calculation and efficient storage of the SM remains an extremely challenging task for currently available clinical tomographs, due to the large number of matrix elements (between 10 13 in small animal PET systems to 10 16 for a standard clinical human PET scanner) and storage requirements (on the orther of TeraBytes), so it needs especial manipulation techniques in real systems (Johnson et al (1995), de la Prieta (2004), Rehfeld & Alber (2007), Ortuño et al (2010)). This is the reason why prototyping languages, such as MATLAB, have not yet offered a solution for 3D realistic sized PET reconstruction (though some freely available MATLAB add-ons for 2D PET reconstruction can be found at http://www.eecs.umich.edu/~fessler/code/ and in the MATLAB Central web page) In this sense, some researchers have shown renewed interest in high performance computing solutions such as PC clusters (Jones et al (2006), Beisel et al (2008)) and Graphic Processing Units (GPUs) ), Zhou & Qi (2011).…”

Influence of Rotation Increments on Imaging Performance for a Rotatory Dual-Head PET System

“…For a stationary dual-head PET system [3, 6–8], the incomplete angle information degrades the spatial resolution perpendicular to the detector heads even if the iteration algorithms are used [9–12]. Some researchers have adopted the rotation operation to solve this problem [13–15]. There are mainly two schemes, rotating the detectors or rotating the object.…”