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Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging. I. (English) Zbl 1119.65112
In the diffuse optical tomography, the discretization error in the numerical solution of the forward and inverse problems results in error in the reconstructed optical images. In this part of the work the authors analyze the error in the reconstructed optical absorption images, resulting from the discretization of the forward and inverse problems. The analysis identifies several factors which influence the extent to which the discretization impacts on the accuracy of the reconstructed images.
[For part II see ibid. 23, No. 3, 1135–1160 (2007; Zbl 1119.65113), reviewed below.]

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