×

zbMATH — the first resource for mathematics

Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging. II. (English) Zbl 1119.65113
In part I [ibid. 23, No. 3, 1115–1133 (2007; Zbl 1119.65112), reviewed above], the error in the reconstructed optical absorption images resulting from the discretization of the forward and inverse problems is analyzed. The analysis leads to two new error estimates, which present the relationship between the optical absorption imaging accuracy and the discretization error in the solutions of the forward and inverse problems. In this part of the work, the authors develop new adaptive discretization schemes for the forward and inverse problems in order to reduce the error in the reconstructed images. Numerical experiments validate the error estimates developed in part I and show the improvement in the accuracy of the reconstructed optical images with the new algorithms.

MSC:
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65N15 Error bounds for boundary value problems involving PDEs
35R30 Inverse problems for PDEs
PDF BibTeX XML Cite
Full Text: DOI