
A stochastic approach to mixed linear and nonlinear inverse problems with applications to seismology
We derive an efficient stochastic algorithm for computational inverse pr...
read it

Stochastic solutions to mixed linear and nonlinear inverse problems
We derive an efficient stochastic algorithm for inverse problems that pr...
read it

Some application examples of minimization based formulations of inverse problems and their regularization
In this paper we extend a recent idea of formulating and regularizing in...
read it

Inverse linear problems on Hilbert space and their Krylov solvability
This monograph is centred at the intersection of three mathematical topi...
read it

An ℓ_p Variable Projection Method for LargeScale Separable Nonlinear Inverse Problems
The variable projection (VarPro) method is an efficient method to solve ...
read it

It was "all" for "nothing": sharp phase transitions for noiseless discrete channels
We establish a phase transition known as the "allornothing" phenomenon...
read it

Shape Reconstruction in Linear Elasticity: Onestep Linearization and Monotonicitybased Regularization
We deal with the shape reconstruction of inclusions in elastic bodies. T...
read it
A stochastic algorithm for fault inverse problems in elastic half space with proof of convergence
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [12]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic halfspace and a slip on that fault have to be reconstructed from noisy surface displacement measurements. With the parameter giving the plane containing the fault denoted by m, we prove that the reconstructed posterior marginal of m is convergent as the number of measurement points and the dimension of the space for discretizing slips increase. Our proof relies on a recent result on the stability of the associated deterministic inverse problem [10], on trace operator theory, and on the existence of exact quadrature rules for a discrete scheme involving the underlying integral operator. The existence of such a discrete scheme was proved by Yarvin and Rokhlin, [16]. Our algorithm models the regularization constant C for the linear part of the inverse problem as a random variable allowing us to sweep through a wide range of possible values. We show in simulations that this is crucial when the noise level is not known. We also show numerical simulations that illustrate the numerical convergence of our algorithm.
READ FULL TEXT
Comments
There are no comments yet.