A hybrid stochastic-deterministic gradient descent algorithm for image reconstruction in cone-beam computed tomography. (22nd February 2016)

• Record Type: Journal Article
• Authors: Karimi, Davood; Ward, Rabab K
• Is Part Of: Biomedical physics & engineering express. Volume 2:Number 1(2016)
• Publication Date: 2016-02-22
• Subjects: image reconstruction -- cone-beam computed tomography -- stochastic gradient descent -- quasi-Newton methods; Medical physics -- Periodicals; Biophysics -- Periodicals; Biomedical engineering -- Periodicals; Medical sciences -- Periodicals; 610.153
• DOI: 10.1088/2057-1976/2/1/015008
• Languages: English
• ISSNs: 2057-1976

Abstract

Abstract: There is a growing interest in algorithms for computed tomography (CT) reconstruction from a small number of projection measurements. In this paper, we propose an algorithm that is based on variance-reduced stochastic gradient descent (SGD). Variance-reduced SGD methods are a new class of stochastic optimization algorithms that have proved highly successful in solving large-scale optimization problems. These algorithms store a copy of the full gradient direction or stochastic gradient directions and use them in building update directions. We propose an algorithm for CT image reconstruction that starts off with variance-reduced SGD updates and gradually increases the batch size. As the algorithm approaches the solution and the batch size grows, the algorithm turns into a limited-memory quasi-Newton algorithm to exploit the curvature information in the vicinity of the solution. We apply the proposed algorithm on simulated and real cone-beam CT projections and compare it with several other algorithms. Our results show that the proposed algorithm is very fast and is able to reconstruct very high-quality images in a small number of iterations.