2004
DOI: 10.1109/tmi.2004.831224
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Regularized Image Reconstruction Algorithms for Positron Emission Tomography

Abstract: We develop algorithms for obtaining regularized estimates of emission means in positron emission tomography. The first algorithm iteratively minimizes a penalized maximum-likelihood (PML) objective function. It is based on standard de-coupled surrogate functions for the ML objective function and de-coupled surrogate functions for a certain class of penalty functions. As desired, the PML algorithm guarantees nonnegative estimates and monotonically decreases the PML objective function with increasing iterations.… Show more

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Cited by 42 publications
(27 citation statements)
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“…The projected density measurements at the recorded 90 lines of sight are reconstructed using TomoPy's penalized maximum likelihood algorithm with weighted linear and quadratic penalties [33]. The result of the reconstruction is a time-resolved ensemble-average density field, ρ(x, y, t), at z = 2 mm downstream of the nozzle tip.…”
Section: Methodsmentioning
confidence: 99%
“…The projected density measurements at the recorded 90 lines of sight are reconstructed using TomoPy's penalized maximum likelihood algorithm with weighted linear and quadratic penalties [33]. The result of the reconstruction is a time-resolved ensemble-average density field, ρ(x, y, t), at z = 2 mm downstream of the nozzle tip.…”
Section: Methodsmentioning
confidence: 99%
“…(2). By these means, matrix inversions involved in (6), (12) and (17) which are now handled by the conjugate gradient method would be avoided.…”
Section: Discussionmentioning
confidence: 99%
“…An alternating optimization is performed where a likelihood estimate is followed by inference of the mixture model [11]. A monotonically decreasing surrogate objective function resulting in a closed form expression is proposed in [12] while the median root prior was also used to impose spatial smoothness and stabilize the solution [13]. Finally, a nonlocal prior was designed [14] where the definition of a pixel's neighborhood is broadened.…”
Section: Introductionmentioning
confidence: 99%
“…The iterative reconstruction algorithms for tomography have demonstrated promising results in the ability to compute high-quality 3D images from less data. In which case, the application of iterative algorithms like the Simultaneous Iterative Reconstruction Technique (SIRT) [20], the Simultaneous Algebraic Reconstruction Technique (SART) [21], or other more complex techniques [22] for tomography reconstruction calculations allows qualitative data to be obtained. The ASTRA Toolbox [23] is a MATLAB and Python platform providing high-performance GPU primitives for 2D and 3D A set of neutron radiography images was collected by a CCD-based detector system with a maximum field of view of 20 cm × 20 cm.…”
Section: Methodsmentioning
confidence: 99%