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Tuesday, May 7th 2019

4:00 pm:

Guzina: Waveform tomography and in particular inverse obstacle scattering are essential to a broad spectrum of scientific and technological disciplines, including sonar and radar imaging, geophysics, oceanography, optics, medical diagnosis, and non-destructive material testing. In general, any relationship between the wavefield scattered by an obstacle and its geometry (or physical characteristics) is nonlinear, which invites two overt solution strategies: (i) linearization via e.g. Born approximation and ray theory, or (ii) pursuit of the nonlinear minimization approach. Over the past two decades, however, a number of sampling methods have emerged that both consider the nonlinear nature of the inverse scattering problem and dispense with iterations. Commonly, these techniques deploy an indicator functional that varies with spatial coordinates of the trial i.e. sampling point, and projects the sensory data (namely observations of the scattered field) onto a functional space reflecting the ‘baseline’ wave motion in a background domain. This indicator functional, designed to reach extreme values when the sampling point strikes the anomaly, can be formulated from either a mathematical or a physical standpoint. An example of the latter methodology is perhaps best exemplified via the topological sensitivity (TS) approach. This talk will cover the idea and experimental validation of the TS methodology in the context of acoustic and elastic waves, including a recent backing of the approach within the framework of catastrophe theory.

Gonella: In this work we illustrate an approach to structural and materials diagnostics revolving around the mechanistic reinterpretation of concepts and methods originated in the fields of signal and image processing and machine learning. Anomalies and defects manifest in the dynamic response of a solid medium as a collection of salient and spatially localized events, which are reflected in the data structure of the response in the form of a set of behaviorally or topologically sparse features. We introduce a model-agnostic and baseline-free methodology that requires virtually no a priori knowledge of the medium’s material properties and forsakes the need for any knowledge of the system's behavior in its pristine state. This agnostic attribute makes the methodology powerful in dealing with media with heterogeneous or unknown property distribution, for which a material model is unsuitable or unreliable. The method revolves around the construction of sparse representations of the dynamic response, which are obtained by learning instructive dictionaries that form a suitable basis for the response data. The resulting sparse coding problem is recast as a modified dictionary-learning task with additional sparsity constraints enforced on the atoms of the dictionaries, which provides them with a prescribed spatial topology designed to unveil potential anomalous regions in the physical domain. The method is validated using synthetically generated data as well as experimental data acquired using a scanning laser Doppler vibrometer.

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