We consider the asymptotic expansion of the solution to a diffusion
equation with a finite number of absorbing inclusions of small
volume. We use the first few terms in this expansion to reconstruct
the absorption of the inclusions and certain geometrical characteristics.
We show that the number of inclusions, their location and their capacity
can be reconstructed in a stable way even from moderately noisy data.
The reconstruction of the absorption parameter requires however
to have far less noisy data. The method of asymptotic expansions of
small volume inclusions provides a useful framework to decide which
information can be reconstructed from boundary measurements with a
given noise level.
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