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Robust reconstruction of fluorescence molecular tomography with an optimized illumination pattern

by Y. Liu and W. Ren and H. Ammari

(Report number 2019-52)

Abstract
Fluorescence molecular tomography (FMT) is an emerging powerful tool for biomedical research and drug development. The reconstruction quality of the unknown fluorescence distribution is the focus of many FMT studies. There are two important factors that influence the quality of reconstruction most effectively. The first one is the regularization techniques used in the inverse model. Traditional methods such as Algebraic Reconstruction Technique and Tikhonov regularization suffer from low spatial resolution and poor signal to noise ratio. We observe that in many cases the target to be imaged is small in size compared to its background, hence, sparse regularization techniques including l1 regularization and l1-l2 joint regularization have been employed to improve the reconstruction quality. The second factor is the illumination pattern. A better illumination pattern ensures the quantity and quality of the information content of the data set thus leading to better reconstructions. However, the design of the optimal illumination pattern is still an open question. In this work, we take advantage of the discrete formulation of the forward problem to give a rigorous definition of an illumination pattern as well as the admissible set of illumination patterns. We add all the restrictions in the admissible set as different types of regularizers to a discrepancy functional, giving rise to another inverse problem with the illumination pattern as unknown. Both inverse problems of reconstructing the fluorescence distribution and finding the optimal illumination pattern are solved by fast efficient iterative algorithms. In the end, we propose a two-step reconstruction strategy which combines the sparse regularization based reconstruction procedure and the design of the optimal illumination pattern process. Numerical experiments have shown that with suitable choice of the regularization parameters the two-step approach converges to an optimal illumination pattern very quickly and remains stable after several rounds of iterations. Regardless of the initial illumination pattern, the reconstructed image based on the optimal illumination pattern proves to have better spatial resolution and higher signal to noise ratio compared to that of an unoptimized illumination pattern.

Keywords: fluorescence molecular tomography, optimal illumination pattern, inverse problem, sparse regularization.

@Techreport{LRA19_856,
  author = {Y. Liu and W. Ren and H. Ammari},
  title = {Robust reconstruction of fluorescence molecular tomography with an optimized illumination pattern},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-52},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-52.pdf },
  year = {2019}
}

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