Characterization of frames for source recovery from dynamical samples
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916108520390656 |
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| author | Aldroubi, Akram Martin, Rocio Diaz Gong, Le Mashreghi, Javad Medri, Ivan |
| author_facet | Aldroubi, Akram Martin, Rocio Diaz Gong, Le Mashreghi, Javad Medri, Ivan |
| contents | 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 $\mathcal{B}(\mathcal{H})$, and $w$ is a source term within a closed subspace $W$ of $\HH$. Our focus is on the stable recovery of $w$ using time-space sample measurements formed by inner products with vectors from a Bessel system $\mathcal{G} \subset \mathcal{H}$. We establish the necessary and sufficient conditions for the recovery of $w$ from these measurements, independent of the unknown initial state $x_0$ and for any $w \in W$. This research is particularly relevant to applications such as environmental monitoring, where precise source identification is critical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of frames for source recovery from dynamical samples Aldroubi, Akram Martin, Rocio Diaz Gong, Le Mashreghi, Javad Medri, Ivan Dynamical Systems Functional Analysis 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 $\mathcal{B}(\mathcal{H})$, and $w$ is a source term within a closed subspace $W$ of $\HH$. Our focus is on the stable recovery of $w$ using time-space sample measurements formed by inner products with vectors from a Bessel system $\mathcal{G} \subset \mathcal{H}$. We establish the necessary and sufficient conditions for the recovery of $w$ from these measurements, independent of the unknown initial state $x_0$ and for any $w \in W$. This research is particularly relevant to applications such as environmental monitoring, where precise source identification is critical. |
| title | Characterization of frames for source recovery from dynamical samples |
| topic | Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2401.15450 |