Related papers: Model selection for inverse problems: Best choice …
We propose numerical algorithms for recovering parameters in eigenvalue problems for linear elasticity of transversely isotropic materials. Specifically, the algorithms are used to recover the elastic constants of a rotor core. Numerical…
We develop a generalized inverse optimization framework for fitting the cost vector of a single linear optimization problem given multiple observed decisions. This setting is motivated by ensemble learning, where building consensus from…
We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…
Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…
The inverse scattering problem on the half-line has been studied in the literature in detail. V. Marchenko presented the solution to this problem. In this paper, the invertibility of the steps of the inversion procedure is discussed and a…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…
The inverse problem methodology is a commonly-used framework in the sciences for parameter estimation and inference. It is typically performed by fitting a mathematical model to noisy experimental data. There are two significant sources of…
In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of…
In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…
One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…