Zobrazeno 1 - 10
of 735
pro vyhledávání: '"Aldroubi, A."'
We investigate the dynamical sampling space-time trade-off problem within a graph setting. Specifically, we derive necessary and sufficient conditions for space-time sampling that enable the reconstruction of an initial band-limited signal on a graph
Externí odkaz:
http://arxiv.org/abs/2411.12670
Autor:
Liu, Xinran, Martín, Rocío Díaz, Bai, Yikun, Shahbazi, Ashkan, Thorpe, Matthew, Aldroubi, Akram, Kolouri, Soheil
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between probability
Externí odkaz:
http://arxiv.org/abs/2410.12176
In this paper, we examine a discrete dynamical system defined by x(n+1) = Ax(n)+ w(n), where x takes values in a Hilbert space H and w is a periodic source with values in a fixed closed subspace W of H. Our goal is to identify conditions on some spat
Externí odkaz:
http://arxiv.org/abs/2408.06934
This paper investigates the problem of recovering source terms in abstract initial value problems (IVP) commonly used to model various scientific phenomena in physics, chemistry, economics, and other fields. We consider source terms of the form $F=h+
Externí odkaz:
http://arxiv.org/abs/2401.15460
In this paper, we address the problem of recovering constant source terms in a discrete dynamical system represented by $x_{n+1} = Ax_n + w$, where $x_n$ is the $n$-th state in a Hilbert space $\mathcal{H}$, $A$ is a bounded linear operator in $\math
Externí odkaz:
http://arxiv.org/abs/2401.15450
In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a differenti
Externí odkaz:
http://arxiv.org/abs/2308.01462
We analyze the problem of recovering a source term of the form $h(t)=\sum_{j}h_j\phi(t-t_j)\chi_{[t_j, \infty)}(t)$ from space-time samples of the solution $u$ of an initial value problem in a Hilbert space of functions. In the expression of $h$, the
Externí odkaz:
http://arxiv.org/abs/2208.13756
We describe a method for signal parameter estimation using the signed cumulative distribution transform (SCDT), a recently introduced signal representation tool based on optimal transport theory. The method builds upon signal estimation using the cum
Externí odkaz:
http://arxiv.org/abs/2207.07989
Publikováno v:
In Linear Algebra and Its Applications 1 August 2024 694:148-185
In this paper, we consider the problem of recovery of a burst-like forcing term in an initial value problem (IVP) in the framework of dynamical sampling. We introduce an idea of using two particular classes of samplers that allow one to predict the s
Externí odkaz:
http://arxiv.org/abs/2109.00623