Related papers: Characterization of frames for source recovery fro…
We develop a linear-programming method to extract dynamical information from static ground-state correlators in quantum field theory. We recast the K\"all\'en-Lehmann inversion as a convex optimization problem, in a spirit similar to the…
When representing convective instability mechanisms with the streamwise BiGlobal stability approach, results suffer from a sensitivity to the streamwise domain truncation length and boundary conditions. The methodology proposed in this…
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…
We study the spectral recovery problem for dynamical sampling on a finite cyclic grid. Given time snapshots obtained from a fixed uniform spatial subsampling of the orbit $x_{\ell}=A^{\ell}f$, we aim to recover the spectrum of the unknown…
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…
We consider lossy compression of an information source when the decoder has lossless access to a correlated one. This setup, also known as the Wyner-Ziv problem, is a special case of distributed source coding. To this day, real-world…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system…
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…
In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…
This paper investigates conditions under which certain kinds of systems of bilinear equations have a unique structured solution. In particular, we look at when we can recover vectors $\boldsymbol{w},\boldsymbol{q}$ from observations of the…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
For a dynamical system, we study the set of points $\cal W$ whose orbit approximates any chosen point at certain specified rates. Our basic setting is that of left shift acting on topological Markov chains endowed with a local weak Gibbs…
Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain…
We study information theoretic limits of recovering an unknown $n$ dimensional, complex signal vector $\mathbf{x}_\star$ with unit norm from $m$ magnitude-only measurements of the form $y_i = |(\mathbf{A} \mathbf{x}_\star)_i|^2, \; i = 1,2…
In phase retrieval we want to recover an unknown signal $\boldsymbol x\in\mathbb C^d$ from $n$ quadratic measurements of the form $y_i = |\langle{\boldsymbol a}_i,{\boldsymbol x}\rangle|^2+w_i$ where $\boldsymbol a_i\in \mathbb C^d$ are…
Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image,…
In many applications, a signal is deformed by well-understood dynamics before it can be measured. For example, when a pollutant enters a river, it immediately begins dispersing, flowing, settling, and reacting. If the pollutant enters at a…
We consider the problem of recovering two unknown vectors, $\boldsymbol{w}$ and $\boldsymbol{x}$, of length $L$ from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with…
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…