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Multivariate form of Hermite sampling series
In this paper, we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial...
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One-bit Sigma-Delta modulation on the circle
Manifold models in data analysis and signal processing have become more prominent in recent years. In this paper, we will look at one of the main...
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Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of \(L^p(\mathbb R^n)\)
The paper is devoted to studying the stability of random sampling in a localized reproducing kernel space. We show that if the sampling set on
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Compressed Data Separation via ℓq-Split Analysis with ℓ∞-Constraint
In this paper, we study compressed data separation (CDS) problem, i.e., sparse data separation from a few linear random measurements. We propose the...
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Phase retrieval and system identification in dynamical sampling via Prony’s method
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with...
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Riemannian optimization for phase retrieval from masked Fourier measurements
In this paper, we consider the noisy phase retrieval problem under the measurements of Fourier transforms with complex random masks. Here two kinds...
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Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system
The Sobolev space H ς (ℝ d ), where ς > d /2, is an important function space that has many applications in various areas of research. Attributed to the...
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Phase retrieval with PhaseLift algorithm
This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been...
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Spectra of rational orthonormal systems
We use the Weyl correspondence approach to investigate the spectral operators of the Laguerre and the Kautz systems. We show that the basic functions...
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A Completeness Theorem for a Hahn–Fourier System and an Associated Classical Sampling Theorem
We introduce a completeness theorem for a Hahn–Fourier-type trigonometric system, where the sine and cosine functions are replaced by
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Sampling for approximating R-limited functions
R -limited functions are multivariate generalization of band-limited functions whose Fourier transforms are supported within a compact region R ⊂ R n ....
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Reconstruction of Splines from Nonuniform Samples
In this paper, we study the reconstruction of spline functions from their nonuniform samples. We investigate the existence and uniqueness of the...
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Double sampling derivatives and truncation error estimates
This paper investigates double sampling series derivatives for bivariate functions defined on R 2 that are in the Bernstein space. For this sampling...
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Phase Retrieval of Real-valued Functions in Sobolev Space
The Sobolev space H s (ℝ d ) with s > d /2 contains many important functions such as the bandlimited or rational ones. In this paper we propose a sequence...
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Dynamical Sampling with Additive Random Noise
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the...
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Linear Reconstructions and the Analysis of the Stable Sampling Rate
The theory of sampling and the reconstruction of data has a wide range of applications and a rich collection of techniques. For many methods a core...
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Sparse recovery in probability via l q -minimization with Weibull random matrices for 0 < q ≤ 1
Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random...
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Sampling in Unitary Invariant Subspaces Associated to LCA Groups
In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA...
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On the Construction of Non-Negative Dimensionality Reduction Methods
Many relevant applications of signal processing rely on the separation of sources from a mixture of signals without prior knowledge about the mixing...
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Sampling with Derivatives in the Bergman Space
We characterize sets of sampling for Bergman space functions and their derivatives. In particular, we show that the methods used in the setting of...