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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…
We consider inverse problems consisting of the reconstruction of an unknown signal $f$ from noisy measurements $y=Ff+\text{noise}$, where $Ff$ is a function on a Riemannian manifold without boundary $\mathcal M$. We consider the case when…
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize so-called reconstructing multiple rank-1 lattices, which combine several preferable…
We consider a mass-conservative fragmentation of the unit interval. The main purpose of this work is to specify the Hausdorff dimension of the set of locations having exactly an exponential decay. The study relies on an additive martingale…
The reconstruction of a function from its spectrogram (i.e., the absolute value of its short-time Fourier transform (STFT)) arises as a key problem in several important applications, including coherent diffraction imaging and audio…
We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. The measurements are made on the entirety of a smooth domain. Since tissues can be modeled as…
The ``Residual-to-Residual DNN series for high-Dynamic range imaging'' (R2D2) approach was recently introduced for Radio-Interferometric (RI) imaging in astronomy. R2D2's reconstruction is formed as a series of residual images, iteratively…
In this paper, an equivalence between existence of particular exponential Riesz bases for multivariate bandlimited functions and existence of certain polynomial interpolants for these bandlimited functions is given. For certain classes of…
Existing results for the estimation of the L\'evy measure are mostly limited to the onedimensional setting. We apply the spectral method to multidimensional L\'evy processes in order to construct a nonparametric estimator for the…
We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…
We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…
Undersampling the k-space during MR acquisitions saves time, however results in an ill-posed inversion problem, leading to an infinite set of images as possible solutions. Traditionally, this is tackled as a reconstruction problem by…
To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
The selective frequency damping method was applied to a bent flow. The method was used in an adaptive formulation. The most dangerous frequency was determined by solving an eigenvalue problem. It was found that one of the patterns,…
In this work, we investigate the sampling and reconstruction of spectrally $s$-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as {randomized} dynamical…