# Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization

## TL;DR

This paper introduces a fluorescence molecular tomography reconstruction method combining sparse initialization with MLEM to effectively model Poisson noise, achieving faster convergence and improved image quality.

## Contribution

The novel approach integrates sparse reconstruction with MLEM, enhancing noise modeling and convergence speed in FMT imaging.

## Key findings

- Over 20 times faster convergence than uniform initialization
- Significant qualitative and quantitative image improvements
- Enhanced robustness to noise in FMT reconstructions

## Abstract

We present a reconstruction method involving maximum-likelihood expectation maximization (MLEM) to model Poisson noise as applied to fluorescence molecular tomography (FMT). MLEM is initialized with the output from a sparse reconstruction-based approach, which performs truncated singular value decomposition-based preconditioning followed by fast iterative shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation for this approach is that sparsity information could be accounted for within the initialization, while MLEM would accurately model Poisson noise in the FMT system. Simulation experiments show the proposed method significantly improves images qualitatively and quantitatively. The method results in over 20 times faster convergence compared to uniformly initialized MLEM and improves robustness to noise compared to pure sparse reconstruction. We also theoretically justify the ability of the proposed approach to reduce noise in the background region compared to pure sparse reconstruction. Overall, these results provide strong evidence to model Poisson noise in FMT reconstruction and for application of the proposed reconstruction framework to FMT imaging.