Mathematical methods in image reconstruction
Mathematical methods in image reconstruction
Marching schemes for inverse acoustic scattering problems
Numerische Mathematik
Asymptotic Imaging of Perfectly Conducting Cracks
SIAM Journal on Scientific Computing
| Hi-index | 0.00 |
We develop a direct (noniterative) algorithm to address the inverse problem of identifying a collection of disjoint internal corrosive parts of small Hausdorff measures in pipelines from exterior ultrasound boundary measurements. The method is based on an asymptotic expansion of the effect of the corrosion in terms of the size of the corrosive parts. We numerically test the validity of the asymptotic formula at high frequencies. We also propose a simple procedure to remove high-frequency instabilities in our inversion procedure. We illustrate our main findings with a variety of computational examples.