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Optical tomography in medical imaging. (English) Zbl 0926.35155

Summary: We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction. We discuss the derivation of the diffusion approximation and other simplifications of the full transport problem. We develop sensitivity relation in both the continuous and discrete case with special concentration on the use of the finite element method. A classification of algorithms is presented, and some suggestions for open problems to be addressed in future research are made.

MSC:

35R30 Inverse problems for PDEs
35Q72 Other PDE from mechanics (MSC2000)
78A45 Diffraction, scattering
92C55 Biomedical imaging and signal processing
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