PDE-constrained fluorescence tomography with the frequency-domain equation of radiative transfer

Hyun Keol Kim, Jong Hwan Lee, Andreas H. Hielscher

Research output: Contribution to journalArticlepeer-review


We present the first fluorescence tomography algorithm that is based on a partial differential equation (PDE) constrained approach. PDE methods have been increasingly employed in many numerical applications, as they often lead to faster and more robust solutions of many inverse problems. In particular, we use a sequential quadratic programming (SQP) method, which allows solving the two forward problems in fluorescence tomography (one for the excitation and one for the emission radiances) and one inverse problem (for recovering the spatial distribution of the fluorescent sources) simultaneously by updating both forward and inverse variables in simultaneously at each of iteration of the optimization process. We evaluate the performance of this approach with numerical and experimental data using a transport-theory frequency-domain algorithm as forward model for light propagation in tissue. The results show that the PDE-constrained approach is computationally stable and accelerates the image reconstruction process up to a factor of 15 when compared to commonly employed unconstrained methods.

Original languageEnglish (US)
Article number5437173
Pages (from-to)793-803
Number of pages11
JournalIEEE Journal on Selected Topics in Quantum Electronics
Issue number4
StatePublished - Jul 2010


  • Fluorescence tomography
  • frequency-domain equation of radiative transfer (ERT)
  • partial differential equation (PDE) constrained optimization
  • sequential quadratic programming (SQP)

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Electrical and Electronic Engineering


Dive into the research topics of 'PDE-constrained fluorescence tomography with the frequency-domain equation of radiative transfer'. Together they form a unique fingerprint.

Cite this