arXiv subjects

Chun-Hsiang Tsou

Publications and source records attributed to Chun-Hsiang Tsou.

5 recordsLinked to original sources

arXiv2026

On the Stability of Inverse Conductivity Problem for Polyhedral Inclusions under a Single Measurement

In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are singularity decomposition for elliptic equations in non-smooth domains, propagation of smallness, and microlocal analysis. Combining these tools, we establish a logarithmic stability estimate for the Hausdorff distance between inclusions in terms of the measurement error.

math.AP↗

arXiv2022

Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunction

In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability result in determining a polygonal scatterer by a single far-field measurement. The argument in establishing the stability result is localized around a corner and can be as well used to produce two highly intriguing implications for invisibility and transmission resonance in the wave scattering theory. In fact, we show that if a generic medium scatterer possesses an admissible corner on its support, then there exists a positive lower bound of the $L^2$-norm of the associated far-field pattern. For the transmission resonance, we discover a quantitative connection between the regularity of the transmission eigenfunction at a corner and its analytic or Fourier extension.

math.AP↗

arXiv2020

On Calderón's inverse inclusion problem with smooth shapes by a single partial boundary measurement

We are concerned with the Calderón inverse inclusion problem, where one intends to recover the shape of an inhomogeneous conductive inclusion embedded in a homogeneous conductivity by the associated boundary measurements. We consider the highly challenging case with a single partial boundary measurement, which constitutes a long-standing open problem in the literature. It is shown in several existing works that corner singularities can help to resolve the uniqueness and stability issues for this inverse problem. In this paper, we show that the corner singularity can be relaxed to be a certain high-curvature condition and derive a novel local unique determination result. To our best knowledge, this is the first (local) uniqueness result in determining a conductive inclusions with general smooth shapes by a single (partial) boundary measurement.

math.AP↗

arXiv2019

Stable determination of polygonal inclusions in Calderón's problem by a single partial boundary measurement

We are concerned with the Calderón problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the support of a convex polygonal inclusion by a single partial boundary measurement. We also derive the uniqueness result in a more general scenario where the conductivities are piecewise constants supported in a nested polygonal geometry. Our methods in establishing the stability and uniqueness results have a significant technical initiative and a strong potential to apply to other inverse boundary value problems.

math.AP↗

arXiv2017

Numerical determination of anomalies in multifrequency electrical impedance tomography

The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper we consider the case where the conductivity distribution is piecewise constant, takes a constant value outside a single smooth anomaly, and a frequency dependent function inside the anomaly itself. Using an original spectral decomposition of the solution of the forward conductivity problem in terms of Poincaré variational eigenelements, we retrieve the Cauchy data corresponding to the extreme case of a perfect conductor, and the conductivity profile. We then reconstruct the anomaly from the Cauchy data. The numerical experiments are conducted using gradient descent optimization algorithms.

math.NA↗