Determination of electrical and geometrical characteristics of mine-like and IED-like targets using new globally convergent inverse algorithms
Abstract
The usefulness of this project for the US Army Research Laboratory (ARL) is indicated in the strong support letter from ARL, which is an Appendix of this proposal. The PI currently has five (5) joint publications with Drs. Anders Sullivan and Lam Nguyen, engineers of ARL, and one joint paper is in preparation. This collaboration will continue, and that letter is signed by Sullivan. In addition, the research group of the PI will provide a ready-to-use software to Sullivan and Nguyen. In this project, a series of substantially new versions of the so-called convexification globally convergent numerical method for Coefficient Inverse Scattering Problems (CISPs) with non-redundant data will be developed both analytically and computationally. They will accurately calculate in the standoff mode the following five (5) properties simultaneously of targets mimicing antipersonnel land mines and improvised explosive devices: (1) dielectric constants, (2) electrical conductivities, (3) locations, (4) shapes of front surfaces of targets, and (5) dependencies of properties of items 1 and 2 on circular frequencies, i.e. dispersion properties. Item 5 is both the most challenging and the least investigated one. We will image shapes of front surfaces only, since we will work only with the backscattering data. The global convergence is the single most important feature of all numerical methods of this project, which significantly distinguishes them from all other algorithms for CISPs with non- redundant data. The PI is unaware about any publication in which all above five items would be computed simultaneously in the standoff mode. Due to the simultaneous computation of all above five items, the new algorithms will be more informative than the current globally convergent numerical methods of the PI, which compute only items 1 and 3. Since the above five items fully characterize both electrical and geometrical properties of those targets and since currently the radar community relies only on the intensities of radar images, then the PI believes that this project might potentially lead to a significant decrease of the current false alarm rate. A similar statement is a part of that support letter of ARL. Numerical testing will be conducted for both computationally simulated and microwave experimental data collected by both the research group of the PI, using a microwave facility of the University of North Carolina at Charlotte, and by ARL. Thus, this is an interdisciplinary project. The research group of the PI is well experienced in working with such experimental data. The convexification method has already demonstrated its high stability and accuracy for microwave experimental data for the most challenging case of targets buried in a sandbox. Now, however, significantly more effective and more informative versions of this method will be developed. Almost all new versions of the convexification will have roots in the idea of the very recent paper of the PI published in J. Inverse and Ill-Posed Problems, 25, 669-685, 2017. The convexification method for a CISP constructs a weighted Tikhonov-like functional J which is strictly convex on an a priori chosen ball of an arbitrary radius R > 0 in an appropriate Hilbert space. The strict convexity is ensured via the presence of the Carleman Weight Function in J. The gradient projection method of the optimization of J converges to the exact solution starting from an arbitrary point of that ball. Since R > 0 is an arbitrary number and the starting point is also an arbitrary one, then this is the global convergence.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1910044
Entities
People
- Michael Klibanov
Organizations
- Army Contracting Command
- United States Army
- University of North Carolina at Chapel Hill