Fast imaging of partially conductive linear cracks using impedance data

  title={Fast imaging of partially conductive linear cracks using impedance data},
  author={Kurt Bryan and Janine Haugh and David McCune},
  journal={Inverse Problems},
We develop two closely-related fast and simple numerical algorithms to address the inverse problem of identifying a collection of disjoint linear cracks in a two-dimensional homogeneous electrical conductor from exterior boundary voltage/current measurements. We allow the possibility that the cracks are partially conductive. Our approach also allows us to determine the actual number of cracks present, as well as make use of one or multiple input fluxes. We illustrate our algorithms with a… 

Figures and Tables from this paper

Non-Destructive Recovery of Voids within a Three Dimensional Domain Using Thermal Imaging
We develop an algorithm capable of detecting the presence of spherical voids in a thermally conducting object. In addition, the process recovers both the radii and locations of each void. Our method
Some novel approaches in modelling and image reconstruction for multi-frequency Electrical Impedance Tomography of the human brain
Novel generic tools were developed in order to enable modelling and non-linear image reconstruction of large-scale problems, such as those arising from the head EIT problem.


This paper describes an algorithm for recovering a collection of linear cracks in a homogeneous electrical conductor from boundary measurements of voltages induced by specified current fluxes. The
Unique Determination of Multiple Cracks by Two Measurements
We study the inverse problem of determining multiple cracks in a planar conductor by electrostatic measurements at the boundary. We prove that two measurements at the boundary suffice to identify
Crack determination from boundary measurements—Reconstruction using experimental data
In this work we assess the effectiveness of Electrical Impedance Tomography for determining the presence and the location of an interior crack from boundary measurements. Electrical Impedance
Identification of 2D cracks by elastic boundary measurements
The purpose of this work is to identify two-dimensional (2D) cracks by means of elastic boundary measurements. A uniqueness result is first proved in the general case, as well as the local
Unique determination of a collection of a finite number of cracks from two boundary measurements
We consider the problem of identification of a collection of a finite number of cracks in a planar domain. It is proved that the location and shape of any finite number of cracks can be determined
Recovery of cracks using a point-source reciprocity gap function
In this work we consider the recovery of internal cracks from boundary measurements. We will use a function that we call point-source reciprocity gap function, which may be obtained as a particular
A semi-explicit algorithm for the reconstruction of 3D planar cracks
This paper deals with a semi-explicit algorithm to reconstruct two-dimensional (2D) segment cracks, or three-dimensional (3D) planar cracks, in the framework of overspecified boundary data. The
Identification of simple poles via boundary measurements and an application of EIT
We consider the problem of identifying simple poles of a meromorphic function by means of the value of the function measured on a circle enclosing those poles. We propose an algorithm for this