Proximal splitting methods for fluorescence molecular tomography

Lei Wang; Yongjun Liu; Hui Huang

doi:10.1117/1.OE.57.11.113105

27 November 2018 Proximal splitting methods for fluorescence molecular tomography

Lei Wang, Yongjun Liu, Hui Huang

Author Affiliations +

Optical Engineering, Vol. 57, Issue 11, 113105 (November 2018). https://doi.org/10.1117/1.OE.57.11.113105

Abstract

The inverse problems in fluorescence molecular tomography involve finding stable and meaningful solutions to under-determined and ill-posed linear systems of equations. A promising approach consists of minimizing an objective function, which includes a quadratic data-fidelity term combined with a nonquadratic and nonsmooth convex regularizer. Choosing ℓ₁-norm as an example of this regularizer, our paper proposes three proximal splitting algorithms for the regularized output least-squares formulation of these problems. We evaluate costs of parameter initialization and reconstruction speeds of the three algorithms that split the original problem in different ways, including two types of techniques based on the forward-backward method and the primal-dual method, respectively. Extensive numerical experiments show that in a wide range of test cases (covering different distances between fluorescent targets, noise levels and numbers of sources), all of the three algorithms perform well and produce very nearly the same reconstructed images, with the primal-dual-type algorithm being significantly faster (in terms of CPU time taken by both initialization and reconstruction) than two variants of the forward-backward-type one, as well as two algorithms with publicly available implementations.

Citation Download Citation

Lei Wang, Yongjun Liu, and Hui Huang "Proximal splitting methods for fluorescence molecular tomography," Optical Engineering 57(11), 113105 (27 November 2018). https://doi.org/10.1117/1.OE.57.11.113105

Received: 3 August 2018; Accepted: 5 November 2018; Published: 27 November 2018

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