Klaus Erhard

Inverse electromagnetic scattering in a two-layered medium with an application to mine detection

The detection of metallic objects is an important application in state-of-the-art security technology. In particular, for humanitarian mine detection the task is to detect objects that are buried in soil. Usually hand-held mine detectors create an electromagnetic pulse via a current in some wire loop and evaluate the scattered electromagnetic field via induction in a receiver loop that is moved together with the sender loop. This receiver signal can then be employed in identifying the location and the shape of metallic objects. Here, we model the full electromagnetic scattering problem in a two-layered medium from a perfectly conducting obstacle using boundary integral equations. The scattered field is modeled via a boundary layer approach and for its kernel the Greens matrix for the two-layered medium is constructed. We establish uniqueness and existence for the solution of the corresponding boundary integral equation. In the second part of the paper, we employ a direct search method for parameter estimation to find the location and size of some simple metallic objects from measurements of the induced voltage for a number of sender–receiver-loop positions.

Four-dimensional cardiac reconstruction from rotational x-ray sequences: first results for 4D coronary angiography

The tomographic reconstruction of the beating heart requires dedicated methods. One possibility is gated reconstruction, where only data corresponding to a certain motion state are incorporated. Another one is motioncompensated reconstruction with a pre-computed motion vector field, which requires a preceding estimation of the motion. Here, results of a new approach are presented: simultaneous reconstruction of a three-dimensional object and its motion over time, yielding a fully four-dimensional representation. The object motion is modeled by a time-dependent elastic transformation. The reconstruction is carried out with an iterative gradient-descent algorithm which simultaneously optimizes the three-dimensional image and the motion parameters. The method was tested on a simulated rotational X-ray acquisition of a dynamic coronary artery phantom, acquired on a C-arm system with a slowly rotating C-arm. Accurate reconstruction of both absorption coefficient and motion could be achieved. First results from experiments on clinical rotational X-ray coronary angiography data are shown. The resulting reconstructions enable the analysis of both static properties, such as vessel geometry and cross-sectional areas, and dynamic properties, like magnitude, speed, and synchrony of motion during the cardiac cycle.

A Numerical Study of the Probe Method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source

Characterization of Cystic Lesions by Spectral Mammography: Results of a Clinical Pilot Study.

\Phi(\cdot,z)

A second pass correction method for calcification artifacts in digital breast tomosynthesis

with source point z to define an indicator function

Breast‐density measurement using photon‐counting spectral mammography

\hat{I}(z)

Generalized Filtered Back-Projection for Digital Breast Tomosynthesis Reconstruction

which can be reconstructed from Cauchy data or far field data. The indicator function

Spectral volumetric glandularity assessment

\hat{I}(z)

Cone-beam artifact reduction using second pass radon space filling

can be shown to blow off when the source point z tends to the boundary

Automatic volumetric glandularity assessment from full field digital mammograms

\partial D