We present an enhancement of the OSEM (ordered set expectation maximization) algorithm for 3D PET reconstruction, which we call the inter-update Metz filtered OSEM (IMF-OSEM). The IMF-OSEM algorithm incorporates filtering action into the image updating process in order to improve the quality of the reconstruction. With this technique, the multiplicative correction image--ordinarily used to update image estimates in plain OSEM--is applied to a Metz-filtered version of the image estimate at certain intervals. In addition, we present a software implementation that employs several high-speed features to accelerate reconstruction. These features include, firstly, forward and back projection functions which make full use of symmetry as well as a fast incremental computation technique. Secondly, the software has the capability of running in parallel mode on several processors. The parallelization approach employed yields a significant speed-up, which is nearly independent of the amount of data. Together, these features lead to reasonable reconstruction times even when using large image arrays and non-axially compressed projection data. The performance of IMF-OSEM was tested on phantom data acquired on the GE Advance scanner. Our results demonstrate that an appropriate choice of Metz filter parameters can improve the contrast-noise balance of certain regions of interest relative to both plain and post-filtered OSEM, and to the GE commercial reprojection algorithm software.
Summary. We present a object-oriented library of C++ features for 3D PET reconstruction. This library has been designed so that it can be used for many algorithms and scanner geometries. Its flexibility, portability and modular design have helped greatly to (a) develop new iterative algorithms, (b) compare iterative and analytic methods using simulated, phantom and patient data, (c) adapt and apply the developed reconstruction algorithms to different designs of tomographs. As 3D iterative reconstruction algorithms are time consuming, the library contains classes and functions to run parts of the reconstruction in parallel, using parallel platforms with a distributed memory architecture.
o r p o i n t m e t h o d (P D) b a s e d optimizer as a robust linear programming (LP) solver is now well established. Instead of replacing the sparse simplex algorithm (SSX), the PD is increasingly seen as complementing it. The progress of PD iterations is not hindered by the degeneracy or the stalling problem of the SSX, indeed it reaches the 'near optimum' solution very quickly. The SSX algorithm, in contrast, is not affected by the boundary conditions which slow down the convergence of the PD. If the solution to the LP problem is non unique, the PD algorithm converges to an interior point of the solution set while the SSX algorithm finds an extreme point solution. To take advantage of the attractive properties of both the PD and the SSX, we have designed a hybrid framework whereby cross over from PD to SSX can take place at any stage of the PD optimization run. The cross over to SSX involves the partition of the PD solution set to active and dormant variables. In this paper we examine the practical difficulties in partitioning the solution set, we discuss the reliability of predicting the solution set partition before optimality is reached and report the results of combining exact and inexact prediction with SSX basis recovery.
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