Adrian Nachman

Conductivity imaging with a single measurement of boundary and interior data

We consider the problem of imaging the conductivity from knowledge of one current and corresponding voltage on a part of the boundary of an inhomogeneous isotropic object and of the magnitude |J(x)| of the current density inside. The internal data are obtained from magnetic resonance measurements. The problem is reduced to a boundary value problem with partial data for the equation ∇ |J(x)||∇u|−1∇u = 0. We show that equipotential surfaces are minimal surfaces in the conformal metric |J|2/(n−1)I. In two dimensions, we solve the Cauchy problem with partial data and show that the conductivity is uniquely determined in the region spanned by the characteristics originating from the part of the boundary where measurements are available. We formulate sufficient conditions on the Dirichlet data to guarantee the unique recovery of the conductivity throughout the domain. The proof of uniqueness is constructive and yields an efficient algorithm for conductivity imaging. The computational feasibility of this algorithm is demonstrated in numerical experiments.

Recovering the conductivity from a single measurement of interior data

We consider the problem of recovering the conductivity of an object from knowledge of the magnitude of one current density field in its interior. A known voltage potential is assumed imposed at the boundary. We prove identifiability and propose an iterative reconstruction procedure. The computational feasibility of this procedure is demonstrated in some numerical experiments.

Current Density Impedance Imaging

Current density impedance imaging (CDII) is a new impedance imaging technique that can noninvasively measure the conductivity distribution inside a medium. It utilizes current density vector measurements which can be made using a magnetic resonance imager (MRI) (Scott et al., 1991). CDII is based on a simple mathematical expression for nablasigma/sigma = nabla ln sigma, the gradient of the logarithm of the conductivity sigma, at each point in a region where two current density vectors J1 and J2 have been measured and J1 x J2 ne 0. From the calculated nabla In sigma and a priori knowledge of the conductivity at the boundary, the logarithm of the conductivity In sigma is integrated by two different methods to produce an image of the conductivity sigma in the region of interest. The CDII technique was tested on three different conductivity phantoms. Much emphasis has been placed on the experimental validation of CDII results against direct bench measurements by commercial LCR meters before and after CDII was performed.

CMOS SOCs at 100 GHz: System Architectures, Device Characterization, and IC Design Examples

This paper investigates the suitability of 90nm and 65nm GP and LP CMOS technology for SOC applications in the 60GHz to 100GHz range. Examples of system architectures and transceiver building blocks are provided which emphasize the need for aggressively scaled GP CMOS and low-VT transistors if CMOS is to compete with SiGe BiCMOS above 60 GHz. This requirement is in conflict with the 2005-ITRS proposal to use LP CMOS for RF applications.

Reconstruction in the Calderon Problem with Partial Data

We consider the problem of recovering the coefficient σ(x) of the elliptic equation ▿·(σ▿u) = 0 in a body from measurements of the Cauchy data on possibly very small subsets of its surface. We give a constructive proof of a uniqueness result by Kenig, Sjöstrand, and Uhlmann. We construct a uniquely specified family of solutions such that their traces on the boundary can be calculated by solving an integral equation which involves only the given partial Cauchy data. The construction entails a new family of Greens functions for the Laplacian, and corresponding single layer potentials, which may be of independent interest.

Reconstruction of Planar Conductivities in Subdomains from Incomplete Data

We consider the problem of recovering a sufficiently smooth isotropic conductivity from interior knowledge of the magnitude of the current density field

A new approach to current density impedance imaging

|J|

Multiscale registration of real-time and prior MRI data for image-guided cardiac interventions.

generated by an imposed voltage potential f on the boundary. In any dimension

Conductivity Imaging from One Interior Measurement in the Presence of Perfectly Conducting and Insulating Inclusions

n\geq2

Current Density Impedance Imaging of an Anisotropic Conductivity in a Known Conformal Class

, we show that equipotential sets are global area minimizers in the conformal metric determined by