Keyword

atomic decomposition

Description: Atomic decomposition is a representation of functions as sums of simple building blocks called atoms, used in harmonic analysis and function-space theory.

Primary topic: Advanced Harmonic Analysis Research (56%)

OpenAlex ID: keywords/atomic-decomposition

Atomic Decomposition by Basis Pursuit

1998 · Scott Shaobing Chen, David L. Donoho, et al. · SIAM Journal on Scientific Computing · 6,845

Atomic Decomposition by Basis Pursuit

2001 · Scott Shaobing Chen, David L. Donoho, et al. · SIAM Review · 5,086

Uncertainty principles and ideal atomic decomposition

2001 · D.L. Donoho, X. Huo · IEEE Transactions on Information Theory · 1,949

A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm

2008 · H. Mohimani, M. Babaie-Zadeh, et al. · IEEE Transactions on Signal Processing · 1,093

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A discrete transform and decompositions of distribution spaces

1990 · Michael Frazier, Björn Jawerth · Journal of Functional Analysis · 994

Recent advances in time–frequency analysis methods for machinery fault diagnosis: A review with application examples

2013 · Zhipeng Feng, Ming Liang, et al. · Mechanical Systems and Signal Processing · 993

Modern Fourier Analysis

2014 · Loukas Grafakos · Graduate texts in mathematics · 950

Banach spaces related to integrable group representations and their atomic decompositions, I

1989 · Hans G Feichtinger, K.H Gröchenig · Journal of Functional Analysis · 704

Weighted Hardy Spaces

1989 · Jan-Olov Strömberg, Alberto Torchinsky · Lecture notes in mathematics · 575

Describing functions: Atomic decompositions versus frames

1991 · Karlheinz Gr�chenig · Monatshefte für Mathematik · 495

Some new function spaces and their applications to Harmonic analysis

1985 · R.R Coifman, Y Meyer, et al. · Journal of Functional Analysis · 477

Martingale Hardy Spaces and their Applications in Fourier Analysis

1994 · Ferenc Weisz · Lecture notes in mathematics · 456

Hardy spaces with variable exponents and generalized Campanato spaces

2012 · Eiichi Nakai, Yoshihiro Sawano · Journal of Functional Analysis · 374

Banach spaces related to integrable group representations and their atomic decompositions. Part II

1989 · Hans G. Feichtinger, K. H. Gr�chenig · Monatshefte für Mathematik · 326

Comparative Analysis of Spectral Approaches to Feature Extraction for EEG-Based Motor Imagery Classification

2008 · Pawel Herman, Girijesh Prasad, et al. · IEEE Transactions on Neural Systems and Rehabilitation Engineering · 322

Interpolation of Besov Spaces

1988 · Ronald A. DeVore, Vasil A. Popov · Transactions of the American Mathematical Society · 289

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Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

2011 · Steve Hofmann, Guozhen Lu, et al. · Memoirs of the American Mathematical Society · 276

ADMiRA: Atomic Decomposition for Minimum Rank Approximation

2010 · Kiryung Lee, Yoram Bresler · IEEE Transactions on Information Theory · 267

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A characterization of $H^{p}(R^{n})$ in terms of atoms

1978 · Robert Latter · Studia Mathematica · 261

A decomposition into atoms of distributions on spaces of homogeneous type

1979 · Roberto A Macías, Carlos Segovia · Advances in Mathematics · 253

Function spaces of variable smoothness and integrability

2009 · L. Diening, P. Hästö, et al. · Journal of Functional Analysis · 231

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Sparse Components of Images and Optimal Atomic Decompositions

2001 · D. L. Donoho · Constructive Approximation · 230

Martingale Spaces and Inequalities

1993 · Ruilin Long · Vieweg+Teubner eBooks · 225

Hardy space $H^1$ associated to Schrödinger operator with potential satisfying reverse Hölder inequality

1999 · Jacek Dziubański, Jacek Zienkiewicz · Revista Matemática Iberoamericana · 222

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A unified approach to atomic decompositions via integrable group representations

1988 · Hans G. Feichtinger, Karlheinz Gröchenig · Lecture notes in mathematics · 221

Works count: 1,701

Citation count: 39,580