Stabilizing Inverse Problems by Internal Data

Details Stabilizing Inverse Problems by Internal Data Stabilizing Inverse Problems by Internal Data

2011-10-09

arxiv.org/abs/1110.1819v3

Mathematics

Analysis of PDEs

The version 3 has been somewhat restructured; section on QPAT was revised and corrected

Scientific paper

Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity and the current) about the parameters of the tissues. This information, in turn, happens to stabilize the exponentially unstable and thus low resolution optical and electrical impedance tomography. Various known instances of this effect have been studied individually. We show that there is a simple general technique (covering all known cases) that shows what kind of interior data stabilizes the reconstruction, and why. Namely, we show when the linearized problem becomes elliptic pseudo-differential one, and thus stable. Stability here is meant as the problem being Fredholm, so the local uniqueness is not shown and probably does not hold in such generality.

Affiliated with

Also associated with

No associations

Rating

Stabilizing Inverse Problems by Internal Data does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stabilizing Inverse Problems by Internal Data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stabilizing Inverse Problems by Internal Data will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-88143