Nonlinear Approximation with Dictionaries I. Direct Estimates

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Banach frames for multivariate α-modulation spaces (2006, methodology): “best m-term approximation, and using the stabillity of the frames, we can apply a general theory introduced in [ 11 ].”
History and Evolution of the Density Theorem for Gabor Frames (2007, background): “range of areas, including, for example, sampling theory [1], operator theory [100], nonlinear sparse approximation [84], pseudodifferential operators [94], wavelet theory [49], wireless communications [171], data transmission with erasures [83], signal processing [24], and quantum computing [58].”
Highly sparse representations from dictionaries are unique and independent of the sparseness measure (2007, unknown): “As K τ ( D ) = D τ (see [28]), it is not diﬃcult to see that a necessary and suﬃcient condition to get map continuously τ into τ .”
Frame Decomposition of Decomposition Spaces (2007, background): “The connection between nonlinear approximation properties and sparse expansions has been studied from an abstract point of view in a number of papers, see for example [33, 14, 25, 28 , 29].”
Bi-framelet systems with few vanishing moments characterize Besov spaces (2004, background): “Proof. First, notice that we have (see [ 14 ]), for 0 < = 1= 1=p < r,”