相关论文: Recovering piecewise smooth functions from nonunif…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
We investigate the problem of reconstructing a 2D piecewise smooth function from its bandlimited Fourier measurements. This is a well known and well studied problem with many real world implications, in particular in medical imaging. While…
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…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…
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…
Many reconstruction problems in signal processing require solution of a certain kind of nonlinear systems of algebraic equations, which we call Prony systems. We study these systems from a general perspective, addressing questions of global…
In this paper we provide a reconstruction algorithm for piecewise-smooth functions with a-priori known smoothness and number of discontinuities, from their Fourier coefficients, posessing the maximal possible asymptotic rate of convergence…
Accurate reconstruction of piecewise-smooth functions from a finite number of Fourier coefficients is an important problem in various applications. The inherent inaccuracy, in particular the Gibbs phenomenon, is being intensively…
In this paper we study the general reconstruction of a compactly supported function from its Fourier coefficients using compactly supported shearlet systems. We assume that only finitely many Fourier samples of the function are accessible…
We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its…
We provide sufficient conditions on a family of functions $(\phi_\alpha)_{\alpha\in A}:\mathbb{R}^d\to\mathbb{R}$ for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in $\mathbb{R}^d$. We consider…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…
Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling.…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…