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Abstract: This
thesis explores the application of complexity penalized algorithms to solve a variety of
geophysical inverse problems: Hydraulic Fracture Monitoring (HFM), hyper-spectral
imaging, and reflection seismology. Through these examples, the thesis examines how the
physics of several systems gives rise to sparsity or low-dimensionality when posed in
the proper basis. This low complexity ... read morecan be quantified into several types of convex
norms such as the L1 and nuclear norm. In this work we demonstrate how optimization
algorithms which exploit this complexity by penalizing the relevant convex norms can
improve inversion. First and second order as well as stochastic algorithms are used to
solve these minimization problems and I give details as to how the structure of the
problem dictates the best technique to apply.
Thesis
(M.S.)--Tufts University, 2013.
Submitted to the
Dept. of Electrical Engineering.
Advisor: Shuchin
Aeron.
Committee: Eric Miller, and Misha
Kilmer.
Keywords: Geophysics, Electrical
engineering, and Applied mathematics.read less
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