Numerical Analysis of Wavelet Methods

By Albert Cohen. 2003

584 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c1d54e62979481354d49bbf48bd863b895c29881

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Citations in the corpus

The Undecimated Wavelet Decomposition and its Reconstruction (2007, background): “Background texts on the wavelet transform include [1]–[5].”
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs (2011, methodology): “We refer to [6] for a detailed treatment of wavelets.”
A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series (2006, methodology): “The associated scaling and wavelet functions φ and ψ satisfy (W-1)–(W-4), where α in (W-2) is a function of M which increases to infinity as M tends to infinity (see [3], Theorem 2.”
Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints (2007, unknown): “A new generation of optimal numerical schemes has been developed for the computation of sparse solutions of differential and integral equations, exploiting adaptive and greedy strategies [12, 13, 14, 16, 17].”
Minimax Testing of a Composite null Hypothesis Defined via a Quadratic Functional in the Model of regression (2012, methodology): “We ﬁrst decompose the empirical coeﬃcients as follows: Then, using standard arguments, we have (cid:13)(cid:13) (cid:13)(cid:13) Furthermore, by well-known properties of wavelet bases (Cohen, 2003) and the Rosenthal inequality, ).”
On adaptive posterior concentration rates (2013, methodology): “We append the basis with boundary conditions and assume that it is associated with a R-regular multiresolution of L2, see Cohen [13] and Cohen et al. [14].”
From Multifractal Measures to Multifractal Wavelet Series (2005, background): “For more details on unconditional characterizations of Besov spaces by wavelet coefficients (in particular when p < 1), see for instance [17, 52].”
Spline interpolation on sparse grids (2011, background): “The following important result is due to Bourdaud [59], but see also Cohen [29] and Lemarie and Kahane [60].”
Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations (2007, background): “The proof of these inequalities and more information on wavelets can be found, e.g., in [2].”
Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression (2015, background): “es that keh h 0k 1= O p(J p=d): Note that Bernstein inequalities (or inverse estimates) from approximation theory imply that k@hk 1= O(Jjj=d)khk 1 for all h2 J (see Schumaker (2007) for splines and Cohen (2003) for wavelets on domains). Therefore, k@eh @h 0k 1k@ eh @( Jh 0)k 1+ k@ ( Jh 0) @ h 0k 1 O”
Two-step regularization methods for linear inverse problems (2006, methodology): “For the exact definition and further results, like the connection to the so-called Strang-Fix conditions, we refer to [3].”