The Inverse Source Problem for Maxwell's Equations

Abstract

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for resiewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)2 SUPPLEMENTARY NOTESFinal report delivered by the AFOSR contractor (Monk) to the government (AFRL/HEX members contributing) based upon EEG data supplied by Dr. James Kroger, New Mexico State University.10-26-06: Cleared for public release; PA-06-382 14. ABSTRACT The inverse source problem for Maxwell's equations is considered. We show that the problem of finding a volume current density from surface measurements does not have a unique solution, and we characterize the nonuniqueness. We also show that if further information is available the inverse source problem may have a unique solution. The method is useful for the quantitative determination of interior brain currents from surface electroencephalographic measurements. The application is to prosthesis control. Abstract. The inverse source problem for Maxwell's equations is considered. We show that the problem of finding a volume current density from surface measurements does not have a unique solution, and characterize the non-uniqueness. We also show that if further a priori information is available, the inverse source problem may have a unique solution (in particular for surface currents or dipole sources). SUBJECT

Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data

“…Motivation for the study of this problem is provided by medical imaging as well as antenna synthesis. In medical application it is desired to use the measurement of the radiated field on the surface of the human brain to infer the abnormalities inside the brain, which produced the measured field [1,5,15,16]. In antenna synthesis, the problem is to find the current distribution along a linear antenna which produces the desired radiated field [4,13].…”

A Direct Sampling Method for Recovering Electromagnetic Dipolar Sources

“…Here we only consider the behavior of I (1) N (z). Other components of I N (z) can be handled analogously.…”

“…Ammari et al [2] obtained a similar result using the tangential components of electric or magnetic field and proposed a numerical method to establish the location of a single dipole. Albanese and Monk [1] studied the unique determination of a volume current source with respect to the boundary tangential components of an electromagnetic fields. Inui and Ohnaka [15] proposed a direct boundary integral based identification method for electric dipoles.…”

A Fourier Method to Recover Elastic Sources with Multi-Frequency Data

“…They occur in various practical applications, including acoustic tomography [3,7,13,15], medical imaging [2,4,10], pollution of environment [8], gesture-computing technology [11,14,16] and have been vigorously studied in recent years. In the fixed frequency case, the inverse source problems possess non-unique solutions due to the presence of a non-radiating source [1,6,12,17]. One of the ways to overcome this difficulty consists in the use of multi-frequency data [5].…”