Ten lectures on wavelets
Two-scale difference equations II. local regularity, infinite products of matrices and fractals
SIAM Journal on Mathematical Analysis
Journal of Multivariate Analysis
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Invariances, Laplacian-like wavelet bases, and the whitening of fractal processes
IEEE Transactions on Image Processing
A wavelet-based KL-like expansion for wide-sense stationary randomprocesses
IEEE Transactions on Signal Processing
Self-Similarity: Part II—Optimal Estimation of Fractal Processes
IEEE Transactions on Signal Processing
Cardinal exponential splines: part I - theory and filtering algorithms
IEEE Transactions on Signal Processing
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In this work, we prove that certain L^2-unbounded transformations of orthogonal wavelet bases generate vaguelets. The L^2-unbounded functions involved in the transformations are assumed to be quasi-homogeneous at high frequencies. We provide natural examples of functions which are not quasi-homogeneous and for which the resulting transformations are not vaguelets. We also address the related question of whether the considered family of functions is a Riesz basis in L^2(R). The Riesz property could be deduced directly from the results available in the literature or, as we outline, by using the vaguelet property in the context of this work. The considered families of functions arise in wavelet-based decompositions of stochastic processes with uncorrelated coefficients.