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Stability of spectral partitions with corners
Gregory Berkolaiko, Yaiza Canzani, Graham Cox +2
A spectral minimal partition of a manifold is a decomposition into disjoint open sets that minimizes a spectral energy functional. While it is known that bipartite minimal partitio…
Half-time Range description for the free space wave operator and the spherical means transform
Peter Kuchment, Leonid Kunyansky
The forward problem arising in several hybrid imaging modalities can be modeled by the Cauchy problem for the free space wave equation. Solution to this problems describes propagat…
Stabilizing inverse problems by internal data. II. Non-local internal data and generic linearized uniqueness
Peter Kuchment, Dustin Steinhauer
In the previous paper "Stabilizing Inverse Problems by Internal Data", the authors introduced a simple procedure that allows one to detect whether and explain why internal informat…
Stabilizing Inverse Problems by Internal Data
Peter Kuchment, Dustin Steinhauer
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior informat…
2D and 3D reconstructions in acousto-electric tomography
Peter Kuchment, Leonid Kunyansky
We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional imped…
Mathematics of Photoacoustic and Thermoacoustic Tomography
Peter Kuchment, Leonid Kunyansky
This is the manuscript of the chapter for a planned Handbook of Mathematical Methods in Imaging that surveys the mathematical models, problems, and algorithms of the Thermoacoustic…