• Publications
  • Influence
Ten Lectures on Wavelets
Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal wavelet bases of compactly supported wavelets and multiresolutional analysis. Expand
  • 14,655
  • 940
Orthonormal bases of compactly supported wavelets
We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the conceptExpand
  • 8,529
  • 504
  • PDF
Ten Lectures on Wavelets.
  • 3,666
  • 497
An Iterative Thresholding Algorithm for Linear Inverse Problems with a Sparsity Constraint
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizingExpand
  • 3,950
  • 373
  • PDF
The wavelet transform, time-frequency localization and signal analysis
  • I. Daubechies
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1 September 1990
Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. Expand
  • 5,844
  • 237
  • PDF
Image coding using wavelet transform
A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. Expand
  • 3,951
  • 151
  • PDF
Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool
Abstract The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in theExpand
  • 993
  • 133
  • PDF
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 simpleExpand
  • 1,054
  • 128
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 underExpand
  • 2,739
  • 98
  • PDF
Iteratively reweighted least squares minimization for sparse recovery
Under certain conditions (known as the restricted isometry property, or RIP) on the mN matrix ˆ (where m<N ), vectors x 2 R N that are sparse (i.e., have most of their entries equal to 0) can beExpand
  • 1,007
  • 88
  • PDF