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Ten Lectures on Wavelets
TLDR
This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
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Orthonormal bases of compactly supported wavelets
TLDR
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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An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
TLDR
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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The wavelet transform, time-frequency localization and signal analysis
TLDR
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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Image coding using wavelet transform
TLDR
A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed and it is shown that the wavelet transform is particularly well adapted to progressive transmission.
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Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool
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Biorthogonal bases of compactly supported wavelets
Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under…
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Factoring wavelet transforms into lifting steps
This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple…
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Iteratively reweighted least squares minimization for sparse recovery
TLDR
It is proved that when Φ satisfies the RIP conditions, the sequence x(n) converges for all y, regardless of whether Φ−1(y) contains a sparse vector.
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Wavelets on the Interval and Fast Wavelet Transforms
We discuss several constructions of orthonormal wavelet bases on the interval, and we introduce a new construction that avoids some of the disadvantages of earlier constructions.
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