קולוקוויום בחוג לגאופיזיקה: Imposing physics-based sparsity in large scale inversion algorithms
Ram Tuvi, Jackson School of Geosciences, the University of Texas at Austin
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.
מארגני האירוע: ד"ר רועי ברקן וד"ר אסף ענבל