For a large class of bounded-error estimation problems, the posterior feasible set S for the parameters can be de…ned by nonlinear inequalities. The set-inversion approach combines classical interval analysis with branch-and-bound algorithms to characterize S. Unfortunately, as bisections have to be done in all directions of the parameter space, this approach is limited to problems involving a ...

Inversion problems have recently drawn vast amounts of attention from the physics community due to their potential widespread applications. In this Rapid Communication, a different type of inversion problem in physics is proposed: an inverse emissivity problem, which aims to determine the emissivity g(nu) by measuring only the total radiated power J(T). Like other inverse problems, this one has...

We propose a new method that uses deep learning techniques to accelerate the popular alternating direction method of multipliers (ADMM) solution for inverse problems. The ADMM updates consist of a proximity operator, a least squares regression that includes a big matrix inversion, and an explicit solution for updating the dual variables. Typically, inner loops are required to solve the first tw...

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which shows how stable the inversion is. If this index is small, then the inversion provides a set of potentials which differ so little, that practically one can re...

The application of the Mobius inversion formula to the specific-heat-phonon spectrum inversion problem (SPI) initially appeared promising [N.X. Chen, Phys. Rev. Lett. 64, 1193 (1990); J. Maddox, Nature (London) 344, 377 (1990)]. However, no one has previously been able to obtain the exact Debye spectrum with the correct cut-off factor and frequency dependence from the Mobius formula. The main d...

Gravity data inversion is one of the important steps in the interpretation of practical gravity data. The inversion result can be obtained by minimization of the Tikhonov objective function. The determination of an optimal regularization parameter is highly important in the gravity data inversion. In this work, an attempt was made to use the active constrain balancing (ACB) method to select the...

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which shows how stable the inversion is. If this index is small, then the inversion provides a set of potentials which differ so little, that practically one can re...

Numerous problems in numerical analysis, including matrix inversion, eigenvalue calculations and polynomial zerofinding, share the following property: The difficulty of solving a given problem is large when the distance from that problem to the nearest "ill-posed" one is small. For example, the closer a matrix is to the set of noninvertible matrices, the larger its condition number with respect...

In applications of inversion methods to real data, nonlinear inverse problems are often simpli ed to more easily solvable linearized inverse problems. By doing so one introduces an error made by the linearization. Nonlinear inverse methods are more accurate because the methods that are used are more correct from a physical point of view. However, if data are used that have a statistical error, ...