Dept. of Geosciences Colloquium: Imposing physics-based sparsity in large scale inversion algorithms

Zoom: https://tau-ac-il.zoom.us/j/89697967497?pwd=YVdOSGpTNmtBOVdOTzNQNEpKTmRSQT09

​Abstract:

Inversion algorithms provide a way to estimate physical properties of an unknown object from a data set. There are numerous applications for these algorithms in medical imaging, computational seismology, target identification, electromagnetic inverse scattering, and subsurface imaging. However, these problems are nonlinear and ill-posed.  Exact numerical algorithms are limited to small scale problems in terms of wavelength. With the increasing computational power, inversion techniques are becoming more efficient for realistic and large-scale problems. To tackle the challenges above, one uses some physical approximations. Still, these problems are often formulated as iterative schemes and contain large data sets. An a priori knowledge of the data is essential to address these algorithms correctly. This utilization must rely on a proper understanding of the wave propagation physics and physics-based signal processing.

In this talk, we present a physics-based sparse data approach for large scale inversion algorithms.  Recent developments in wave technology have enabled us to gather reliable data, which provides a high degree of spatial resolution of the propagation environment. We present both forward and inverse models including a derivation of analytical models for the measured data. We show a direct relationship between the data and specific targets. This relation enables an a-priori sparse representation of the inverse problem, which leads to fast, robust, and efficient algorithms. We demonstrate these features with several numerical examples. 
 

Event Organizers: Dr. Roy Barkan and Dr. Asaf Inbal