Related papers: Sampling the flow of a bandlimited function
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators…
Acquiring temporally high-frequency and spatially high-resolution turbulent wake flow fields in particle image velocimetry (PIV) experiments remains a significant challenge due to hardware limitations and measurement noise. In contrast,…
Reconstructing high-quality magnetic resonance images (MRI) from undersampled raw data is of great interest from both technical and clinical point of views. To this date, however, it is still a mathematically and computationally challenging…
Let $I=(a,b)\times(c,d)\subset {\mathbb R}_{+}^2$ be an index set and let $\{G_{\alpha}(x) \}_{\alpha \in I}$ be a collection of Gaussian functions, i.e. $G_{\alpha}(x) = \exp(-\alpha_1 x_1^2 - \alpha_2 x_2^2)$, where $\alpha = (\alpha_1,…
Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce the acquisition times, reconstruction…
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…
In this work, we consider "finite bandwidth" reproducing kernel Hilbert spaces which have orthonormal bases of the form $f_n(z)=z^n \prod_{j=1}^J \left( 1 - a_{n}w_j z \right)$, where $w_1 ,w_2, \ldots w_J $ are distinct points on the…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
In this paper, the focus is on the reconstruction of a diffusive field and the localization of the underlying driving sources on arbitrary graphs by observing a significantly smaller subset of vertices of the graph uniformly in time.…
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…
We investigate time encoding as an alternative method to classical sampling, and address the problem of reconstructing classes of non-bandlimited signals from time-based samples. We consider a sampling mechanism based on first filtering the…
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…
Let $\lambda$ be a positive number, and let $(x_j:j\in\mathbb Z)\subset\mathbb R$ be a fixed Riesz-basis sequence, namely, $(x_j)$ is strictly increasing, and the set of functions $\{\mathbb R\ni t\mapsto e^{ix_jt}:j\in\mathbb Z\}$ is a…
In this paper we study the sampling recovery problem for certain relevant multivariate function classes which are not compactly embedded into $L_\infty$. Recent tools relating the sampling numbers to the Kolmogorov widths in the uniform…
Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning…
We consider the stable reconstruction of flow geometry and wall shear stress from measurements obtained by magnetic resonance imaging. As noted in a review article by Petersson, most approaches considered so far in the literature seem not…
Estimation of the initial state of turbulent channel flow from limited data is investigated using an adjoint-variational approach. The data are generated from a reference direct numerical simulation (DNS) which is sub-sampled at different…
Let $(F_t)$ be a smooth flow on a smooth manifold $M$ and $h:M\to M$ be a smooth orbit preserving map. The following problem is studied: suppose that for every point $z$ of $M$ there exists a germ of a smooth function $f_z$ at $z$ such that…