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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 21 — Oct. 12, 2009
  • pp: 18433–18448

Application of a wavelet-Galerkin method to the forward problem resolution in fluorescence Diffuse Optical Tomography

Anne Landragin-Frassati, Stéphane Bonnet, Anabela Da Silva, Jean-Marc Dinten, and Didier Georges  »View Author Affiliations

Optics Express, Vol. 17, Issue 21, pp. 18433-18448 (2009)

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Fluorescence diffuse optical tomography is a powerful tool for the investigation of molecular events in studies for new therapeutic developments. Here, the emphasis is put on the mathematical problem of tomography, which can be formulated in terms of an estimation of physical parameters appearing as a set of Partial Differential Equations (PDEs). The standard polynomial Finite Element Method (FEM) is a method of choice to solve the diffusion equation because it has no restriction in terms of neither the geometry nor the homogeneity of the system, but it is time consuming. In order to speed up computation time, this paper proposes an alternative numerical model, describing the diffusion operator in orthonormal basis of compactly supported wavelets. The discretization of the PDEs yields to matrices which are easily computed from derivative wavelet product integrals. Due to the shape of the wavelet basis, the studied domain is included in a regular fictitious domain. A validation study and a comparison with the standard FEM are conducted on synthetic data.

© 2009 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(100.7410) Image processing : Wavelets
(170.3880) Medical optics and biotechnology : Medical and biological imaging

ToC Category:
Medical Optics and Biotechnology

Original Manuscript: July 20, 2009
Revised Manuscript: September 4, 2009
Manuscript Accepted: September 8, 2009
Published: September 28, 2009

Anne Landragin-Frassati, Stéphane Bonnet, Anabela Da Silva, Jean-Marc Dinten, and Didier Georges, "Application of a wavelet-Galerkin method to the forward problem resolution in fluorescence diffuse optical tomography," Opt. Express 17, 18433-18448 (2009)

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