Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography

Abstract

A new class of fast maximum-likelihood estimation (MLE) algorithms for emission computed tomography (ECT) is developed. In these cyclic iterative algorithms, vector extrapolation techniques are integrated with the iterations in gradient-based MLE algorithms, with the objective of accelerating the convergence of the base iterations. This results in a substantial reduction in the effective number of base iterations required for obtaining an emission density estimate of specified quality. The mathematical theory behind the minimal polynomial and reduced rank vector extrapolation techniques, in the context of emission tomography, is presented. These extrapolation techniques are implemented in a positron emission tomography system. The new algorithms are evaluated using computer experiments, with measurements taken from simulated phantoms. It is shown that, with minimal additional computations, the proposed approach results in substantial improvement in reconstruction.

An Improved Maximum Likelihood Approach to Image Reconstruction Using Ordered Subsets and Data Subdivisions

“…One of the main reasons for this is that EM algorithms have very slow convergence speed and thus a large number of iterations may be required to obtain an acceptable reconstructed Manuscript image. Several modifications have been suggested to accelerate the convergence of these algorithms using line search [11] and vector extrapolation [14] techniques. Other fast alternatives have also been proposed to speed up the convergence.…”

Adaptively altering hyper-parameter for improved reconstruction in PET

“…The object space is a square region inscribed within the circle of detectors. To exploit the eight-fold symmetry we have assumed the object to be bounded by a circle inscribed in this square object space [10] [11]. An electron-positron annihilation event occurring inside a pixel is governed by a number of physical phenomena such as attenuation, scattering, absorption and detector characteristics.…”

“…It is found that using symmetry available in the system the data size of P matrix can be reduced considerably [10]. For simulating measurement data, a Monte Carlo procedure is used [1] [11]. Shepp and Logan mathematical phantom with 100,000 emissions has been used for simulation studies.…”

Hybrid prior method for positron emission tomographic image reconstruction

“…Each element of probability matrix pi, is the probability of an annihilation event in pixel i, getting detected in the j t h detector and is taken as the angle seen by the center of pixel i into the detector tube j . For simulating measurement data, a Monte Carlo procedure is used [1] [9]. Shepp-Logan mathematical phantom with 100,000 emissions has been used for the present simulation studies.…”