Related papers: Sharp results on sampling with derivatives in band…
We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure,…
We tensorize the Faber spline system from [14] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. The respective basis coefficients are local linear combinations of discrete function values…
We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain,…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…
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…
Consider the task of sampling and reconstructing a bandlimited spatial field in $\Re^2$ using moving sensors that take measurements along their path. It is inexpensive to increase the sampling rate along the paths of the sensors but more…
This paper deals with the problem of reconstructing a band-limited signal when a finite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for…
This paper investigates signal prediction through the perfect reconstruction of signals from shift-invariant spaces using nonuniform samples of both the signal and its derivatives. The key advantage of derivative sampling is its ability to…
The paper investigates possibility of recovery of sequences from their decimated subsequences. It is shown that this recoverability is associated with certain spectrum degeneracy of a new kind, and that a sequences of a general kind can be…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
Many engineering, social, and biological complex systems consist of dynamical elements connected via a large-scale network. Monitoring the network's dynamics is essential for a variety of maintenance and scientific purposes. Whilst we…
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…
In this work, we study the properties of sampling sets on families of large graphs by leveraging the theory of graphons and graph limits. To this end, we extend to graphon signals the notion of removable and uniqueness sets, which was…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
It is known that the simple slice sampler has robust convergence properties, however the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to…
A new lower bound on the average reconstruction error variance of multidimensional sampling and reconstruction is presented. It applies to sampling on arbitrary lattices in arbitrary dimensions, assuming a stochastic process with constant,…
We study the problem of distinguishing between two symmetric probability distributions over $n$ bits by observing $k$ bits of a sample, subject to the constraint that all $k-1$-wise marginal distributions of the two distributions are…