Related papers: Sampling trajectories for the short-time Fourier t…
Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional…
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…
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…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
Finite time-vertex graph signals (FTVGS) provide an efficient representation for capturing spatio-temporal correlations across multiple data sources on irregular structures. Although sampling and reconstruction of FTVGS with known spectral…
In this article we propose a dynamic approach to complex vector reconstruction in the context of quantum tomography. There are two underlying assumptions behind our reasoning. The first one claims that the evolution of a d-level pure…
We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a…
We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…
Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. However, traditional optimization-based reconstruction is slow and can not yield an exact image in practice. Deep learning-based reconstruction has been a…
In this article we study the retrospective inverse problem. The retrospective inverse problem consists of in the reconstruction of a priori unknown initial condition of the dynamic system from its known final condition. Existence and…
We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the…
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
In this paper, we consider the problem of reconstructing piece-wise smooth functions from their non-uniform Fourier data. We first extend the filter method for uniform Fourier data to the non-uniform setting by using the techniques of…
We analyze data from direct numerical simulations of homogeneous and isotropic turbulence (at Re_\lambda \approx 280) and study the statistics of curvature and torsion of Lagrangian trajectories in order to extract informations on the…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
Compressed sensing theory indicates that selecting a few measurements independently at random is a near optimal strategy to sense sparse or compressible signals. This is infeasible in practice for many acquisition devices that acquire…
Sampling-based algorithms are widely used for motion planning in high-dimensional configuration spaces. However, due to low sampling efficiency, their performance often diminishes in complex configuration spaces with narrow corridors.…
In this paper, we present new regularized Shannon sampling formulas related to the special affine Fourier transform (SAFT). These sampling formulas use localized sampling with special compactly supported window functions, namely B-spline,…
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…