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We introduce a maximal inequality for a local empirical process under strongly mixing data. Local empirical processes are defined as the (local) averages $\frac{1}{nh}\sum_{i=1}^n \mathbf{1}\{x - h \leq X_i \leq x+h\}f(Z_i)$, where $f$…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
We study the large-width asymptotics of random fully connected neural networks with weights drawn from $\alpha$-stable distributions, a family of heavy-tailed distributions arising as the limiting distributions in the Gnedenko-Kolmogorov…
The paper considers recovery of signals from incomplete observations and a problem of determination of the allowed quantity of missed observations, i.e. the problem of determination of the size of the uniqueness sets for a given data…
This paper discusses sample allocation problem (SAP) in frequency-domain Compressive Sampling (CS) of time-domain signals. An analysis that is relied on two fundamental CS principles; the Uniform Random Sampling (URS) and the Uncertainty…
This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…
The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function outside the interval. In a previous paper we discussed the…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is…
Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker--Kotel'nikov--Shannon (WKS) sampling restoration sum for Bernstein function classes $B_{\pi,d}^q,\, q>1,\, d\in \mathbb N$, when…
Suppose that $n$ statistical units are observed, each following the model $Y(x_j)=m(x_j)+ \epsilon(x_j),\, j=1,...,N,$ where $m$ is a regression function, $0 \leq x_1 <...<x_N \leq 1$ are observation times spaced according to a sampling…
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…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
In many textbooks on Generalized Functions and Distributions, we can find an example of infinitely differentiable function of bounded support from space D, called a bump function. This example is incorrect since this function is not…
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…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
It has been shown recently that graph signals with small total variation can be accurately recovered from only few samples if the sampling set satisfies a certain condition, referred to as the network nullspace property. Based on this…
Resampling is an operation costly in calculation time and accuracy. It regularizes irregular sampling, replacing N data by N periodic estimations. This stage can be suppressed, using formulas built with incoming data and completed by…