Related papers: On Weak Observability For Evolution Systems with S…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
In this paper we examine a mutual control problem for systems of two abstract evolution equations subject to a proportionality final condition. Related observability and semi-observability problems are discussed. The analysis employs a…
Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1…
We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
In this paper, we derive explicit reconstruction formulas for two common measurement geometries: a plane and a sphere. The problem is formulated as inverting the forward operator $R^a$, which maps the initial source to the measured wave…
We briefly discuss the problem of specifying initial conditions for evolution of off-diagonal (skewed) parton distributions. We present numerical results to show that evolution rapidly washes out differences of input.
Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…
We propose a novel recursive system identification algorithm for linear autoregressive systems with skewed innovations. The algorithm is based on the variational Bayes approximation of the model with a multivariate normal prior for the…
This paper concerns spectral stability of nonlinear waves in KdV-type evolution equations. The relevant eigenvalue problem is defined by the composition of an unbounded self-adjoint operator with a finite number of negative eigenvalues and…
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…
A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…
The article deals with the problem of synthesis of an adaptive observer of state variables of a linear time-varying SISO dynamic system. It is assumed that the control signal and the output variable are measurable. It is assumed that the…
Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors.…
A common problem in the sciences is that a signal of interest is observed only indirectly, through smooth functionals of the signal whose values are then obscured by noise. In such inverse problems, the functionals dampen or entirely…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by generative adversarial networks, or GANs). In this work,…
In this paper, a concurrent learning based adaptive observer is developed for a class of second-order linear time-invariant systems with uncertain system matrices. The developed technique yields an exponentially convergent state estimator…