Summary: Ultrasound Imaging of Internal Corrosion
We develop a non-iterative method 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 asymp-
totic 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.
Mathematics subject classification (MSC2000): 35R30
Keywords: corrosion, asymptotic representation formula, reconstruction, ultrasound detection, high fre-
quencies, MUSIC-type algorithm
Corrosion detection remains a topic of considerable activity in the inverse problems commu-
nity. Of special interest are algorithms that make use of a priori information or assumptions