Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion

Abstract

Fluorescence molecular tomography (FMT) is a promising imaging modality that enables three-dimensional visualization of fluorescent targets in vivo in small animals. L2-norm regularization methods are usually used for severely ill-posed FMT problems. However, the smoothing effects caused by these methods result in continuous distribution that lacks high-frequency edge-type features and hence limits the resolution of FMT. In this paper, the sparsity in FMT reconstruction results is exploited via compressed sensing (CS). First, in order to ensure the feasibility of CS for the FMT inverse problem, truncated singular value decomposition (TSVD) conversion is implemented for the measurement matrix of the FMT problem. Then, as one kind of greedy algorithm, an ameliorated stagewise orthogonal matching pursuit with gradually shrunk thresholds and a specific halting condition is developed for the FMT inverse problem. To evaluate the proposed algorithm, we compared it with a TSVD method based on L2-norm regularization in numerical simulation and phantom experiments. The results show that the proposed algorithm can obtain higher spatial resolution and higher signal-to-noise ratio compared with the TSVD method.