Thanh Nguyenhttps://works.bepress.com/thanh-nguyen/Recent works by Thanh Nguyenen-usCopyright (c) 2019 All rights reserved.Sun, 01 Mar 2015 00:00:00 +00003600Regularized recursive Newton-type methods for inverse scattering problems using multifrequency measurementshttps://works.bepress.com/thanh-nguyen/4/<div class="line" id="line-7">We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of scattered waves associated with incident plane waves sent from one incident direction but at multiple frequencies. We define, at each frequency, observable shapes as the ones which are described by finitely many modes and produce far field patterns close to the measured one. Our analysis consists of two steps. In the first step, we propose a regularized recursive Newton method for the reconstruction of an observable shape at the highest frequency knowing an estimate of an observable shape at the lowest frequency. We formulate conditions under which an error estimate in terms of the frequency step, the number of Newton iterations, and noise level can be proved. In the second step, we design a multilevel Newton method which has the same accuracy as the one described in the first step but with weaker assumptions on the quality of the estimate of the observable shape at the lowest frequency and a small frequency step (or a large number of Newton iterations). The performances of the proposed algorithms are illustrated with numerical results using simulated data.</div>Mourad Sini et al.Sun, 01 Mar 2015 00:00:00 +0000https://works.bepress.com/thanh-nguyen/4/Journal ArticlesImaging of Buried Objects from Experimental Backscattering Time-Dependent Measurements Using a Globally Convergent Inverse Algorithmhttps://works.bepress.com/thanh-nguyen/2/<div class="line" id="line-7">We consider the problem of imaging of objects buried under the ground using experimental backscattering time-dependent measurements generated by a single point source or one incident plane wave. In particular, we estimate dielectric constants of these objects using the globally convergent inverse algorithm of Beilina and Klibanov. Our algorithm is tested on experimental data collected using a microwave scattering facility at the University of North Carolina at Charlotte. There are two main challenges in working with this type of experimental data: (i) there is a huge misfit between these data and computationally simulated data, and (ii) the signals scattered from the targets may overlap with and be dominated by the reflection from the ground's surface. To overcome these two challenges, we propose new data preprocessing steps to make the experimental data look similar to the simulated data, as well as to remove the reflection from the ground's surface. Results of a total of 25 data sets of both nonblind and blind targets indicate good accuracy.</div>Thanh T. Nguyen et al.Thu, 01 Jan 2015 00:00:00 +0000https://works.bepress.com/thanh-nguyen/2/Journal ArticlesRecovering Dielectric Constants of Explosives via a Globally Strictly Convex Cost Functionalhttps://works.bepress.com/thanh-nguyen/3/<div class="line" id="line-7">The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential equation. After applying the Laplace transform, a new cost functional is constructed and a variational problem is formulated. The key feature of this functional is the presence of the Carleman weight function for the Laplacian. The strict convexity of this functional on a bounded set in a Hilbert space of an arbitrary size is proven. This allows for establishing the global convergence of the gradient descent method. Some results of numerical experiments are presented.</div>Michael Klibanov et al.Thu, 01 Jan 2015 00:00:00 +0000https://works.bepress.com/thanh-nguyen/3/Journal ArticlesReconstruction of the Refractive Index from Experimental Backscattering Data Using a Globally Convergent Inverse Methodhttps://works.bepress.com/thanh-nguyen/5/<div class="line" id="line-7">The problem to be studied in this work is within the context of coefficient identification problems for the wave equation. More precisely, we consider the problem of reconstruction of the refractive index (or equivalently, the dielectric constant) of an inhomogeneous medium using one backscattering boundary measurement. The goal of this paper is to analyze the performance of the globally convergent algorithm of Beilina and Klibanov on experimental data collected using a microwave scattering facility at the University of North Carolina at Charlotte. The main challenge in working with experimental data is the huge misfit between these data and computationally simulated data. We present data preprocessing steps to make the former somehow look similar to the latter. Results of both nonblind and blind targets are shown that indicate good reconstructions even for high contrasts between the targets and the background medium.</div>Thanh T. Nguyen et al.Wed, 01 Jan 2014 00:00:00 +0000https://works.bepress.com/thanh-nguyen/5/Journal Articles