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Linearized Reconstruction for Diffuse Optical Spectroscopic Imaging

by H. Ammari and B. Jin and W. Zhang

(Report number 2018-30)

Abstract
In this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is based on linearization and group sparsity, which allows recovering the diffusion coefficient and absorption coefficient simultaneously, provided that their spectral profiles are incoherent and a sufficient number of wavelengths are judiciously taken for the measurements. We also discuss the reconstruction for imperfectly known boundary and show that with the multi-wavelength data, the method can reduce the influence of modelling errors and still recover the absorption coefficient. Extensive numerical experiments are presented to support our analysis.

Keywords: Diffuse optical spectroscopic imaging, reconstruction algorithm, group sparsity, imperfectly known boundary.

@Techreport{AJZ18_784,
  author = {H. Ammari and B. Jin and W. Zhang},
  title = {Linearized Reconstruction for Diffuse Optical Spectroscopic Imaging},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-30},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-30.pdf },
  year = {2018}
}

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