Stochastic EM methods with Variance Reduction for Penalised PET Reconstructions

TL;DR

This paper introduces variance reduction techniques to accelerate penalised PET image reconstruction algorithms, significantly improving convergence speed and accuracy over traditional methods like OSEM.

Contribution

It proposes novel stochastic EM algorithms with variance reduction, extending classical EM and OSEM methods for faster penalised PET reconstructions.

Findings

Significant acceleration over traditional OSEM methods.

Improved accuracy in penalised PET reconstructions.

Potential for practical clinical application.

Abstract

Expectation-maximization (EM) is a popular and well-established method for image reconstruction in positron emission tomography (PET) but it often suffers from slow convergence. Ordered subset EM (OSEM) is an effective reconstruction algorithm that provides significant acceleration during initial iterations, but it has been observed to enter a limit cycle. In this work, we investigate two classes of algorithms for accelerating OSEM based on variance reduction for penalised PET reconstructions. The first is a stochastic variance reduced EM algorithm, termed as SVREM, an extension of the classical EM to the stochastic context, by combining classical OSEM with insights from variance reduction techniques for gradient descent. The second views OSEM as a preconditioned stochastic gradient ascent, and applies variance reduction techniques, i.e., SAGA and SVRG, to estimate the update direction. We present several numerical experiments to illustrate the efficiency and accuracy of the approaches. The numerical results show that these approaches significantly outperform existing OSEM type methods for penalised PET reconstructions, and hold great potential.