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Nonsmooth, nonconvex regularizers applied to linear elctromagnetic inverse problems
  • Hugo Hidalgo,
  • Enrique Gomez-Trevino
Hugo Hidalgo

Corresponding Author:[email protected]

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Enrique Gomez-Trevino
Centro de Investigacion Cientifica y de Educacion Superior de Ensenada
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Tikhonov’s regularization method is the standard technique applied to obtain models of the subsurface conductivity dis- tribution from electric or electromagnetic measurements by solving UT (m) = ||F(m) - d||^2 + P(m): The second term correspond to the stabilizing functional, with P(m) = ||m||^2 the usual approach, and the regularization parameter. Due to the roughness penalizer inclusion, the model developed by Tikhonov’s algorithm tends to smear discontinuities, a feature that may be undesirable. An important requirement for the regularizer is to allow the recovery of edges, and smooth the homogeneous parts. As is well known, Total Variation (TV) is now the standard approach to meet this requirement. Recently, Wang et.al. proved convergence for alternating direction method of multipliers in nonconvex, nonsmooth optimization. In this work we present a study of several algorithms for model recovering of Geosounding data based on Inmal Convolution, and also on hybrid, TV and second order TV and nonsmooth, nonconvex regularizers, observing their performance on synthetic and real data. The algorithms are based on Bregman iteration and Split Bregman method, and the geosounding method is the low-induction numbers magnetic dipoles. Non-smooth regularizers are considered using the Legendre-Fenchel transform.