Stochastic EM methods with variance reduction for penalised PET reconstructions. (22nd October 2021)

• Record Type: Journal Article
• Authors: Kereta, Željko; Twyman, Robert; Arridge, Simon; Thielemans, Kris; Jin, Bangti
• Is Part Of: Inverse problems. Volume 37:Number 11(2021)
• Publication Date: 2021-10-22
• Subjects: positron emission tomography -- stochastic gradient -- variance reduction -- expectation maximization -- ordered subset expectation maximisation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac2d74
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Expectation-maximisation (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 that combines classical OSEM with 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.