A class of nonharmonic Fourier series
R. J. Duffin,A. C. Schaeffer +1 more
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This article is published in Transactions of the American Mathematical Society.The article was published on 1952-02-01 and is currently open access. It has received 2320 citations till now. The article focuses on the topics: Fourier sine and cosine series & Discrete Fourier series.read more
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A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
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Orthonormal bases of compactly supported wavelets
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
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The wavelet transform, time-frequency localization and signal analysis
TL;DR: Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied and the notion of time-frequency localization is made precise, within this framework, by two localization theorems.
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An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint
TL;DR: It is proved that replacing the usual quadratic regularizing penalties by weighted 𝓁p‐penalized penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem.
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An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
Abstract: We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the coefficients of such expansions, with 1 < or = p < or =2, still regularizes the problem. If p < 2, regularized solutions of such l^p-penalized problems will have sparser expansions, with respect to the basis under consideration. To compute the corresponding regularized solutions we propose an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. We also review some potential applications of this method.
References
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The theory of functions
TL;DR: Alfaro et al. as mentioned in this paper conservado en la Biblioteca del Campus de Mostoles de la Universidad Rey Juan Carlos (sign. 517.5 TIT THE).
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Fourier Transforms in the Complex Domain
TL;DR: In this article, a generalized harmonic analysis in the complex domain of random functions has been proposed, based on Szasz's theorem and a class of singular integral equations of the exponential type.
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Theory of Functions
TL;DR: In this paper, the authors pointed out that the distinction between "finite" and "infinite" is one which does not require definition, and that the authors' view is not the only accepted view.
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Fonctions entières et intégrales de Fourier multiples
Michel Plancherel,G. Plya +1 more