Related papers: Optimal use of time dependent probability density …
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…
A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods.…
In this paper, we consider an inverse problem to determine a source term in a parabolic equation, where the data are obtained at a certain time. In general, this problem is ill-posed, therefore the Tikhonov regularization method is proposed…
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…
In this paper we propose a new statistical stopping rule for constrained maximum likelihood iterative algorithms applied to ill-posed inverse problems. To this aim we extend the definition of Tikhonov regularization in a statistical…
This paper examines issues of data completion and location uncertainty, popular in many practical PDE-based inverse problems, in the context of option calibration via recovery of local volatility surfaces. While real data is usually more…
In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…
Integral equations frequently arise in surface science, and in some cases, they must be treated as inverse problems. In our previous work on optical tweezers, atomic force microscopy, and surface force measurement apparatus, we performed…
We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of…
From the viewpoint of inverse problem, the optimization of drug release based on the multi-laminated drug controlled release devices has been regarded as the solution problem of the diffusion equation initial value inverse problem. In view…
Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…
A critical decision process in data acquisition for mineral and energy resource exploration is how to efficiently combine a variety of sensor types and to minimize total cost. We propose a probabilistic framework for multi-objective…
We exploit the similarities between Tikhonov regularization and Bayesian hierarchical models to propose a regularization scheme that acts like a distributed Tikhonov regularization where the amount of regularization varies from component to…
Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov…
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…
This paper tackles the data completion problem related to the Helmholtz equation. The goal is to identify unknown boundary conditions on parts of the boundary that cannot be accessed directly, by making use of measurements collected from…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…