Ingrid Daubechies

Ingrid Daubechies is a Belgian-American mathematician whose work established compactly supported orthonormal wavelets and helped make wavelet analysis practical.

Wavelet: A function used to analyze signals at multiple scales by shifting and dilating it. Her work developed wavelets with orthogonality and finite support.
Daubechies wavelet: A family of compactly supported orthonormal wavelets constructed by Ingrid Daubechies. These wavelets are the signature mathematical objects of her work.
Alberto Calderón: An Argentine-American mathematician whose work in harmonic analysis influenced modern wavelet theory. Calderón's reproducing formula helped establish mathematical foundations later developed in wavelet analysis.
JPEG 2000: An image-compression standard based on the discrete wavelet transform. Its lossy and lossless coding options use wavelet transforms related to her compactly supported constructions.
Fourier analysis: A method for representing functions as sums of sinusoidal frequencies. Wavelets address limitations of frequency-only descriptions by retaining information about location.
Quadrature mirror filter: A pair of digital filters designed to split and reconstruct signal frequency bands without loss. Filter coefficients encode the scaling function and wavelet in practical algorithms.
Yves Meyer: A French mathematician who made foundational contributions to wavelet theory and multiresolution analysis. Meyer's wavelet constructions formed part of the research context for Daubechies's work.
Image compression: The reduction of digital image data while preserving information needed for storage or display. Wavelet representations can concentrate image information into relatively few coefficients.
Orthogonality: A relation between functions or vectors whose inner product is zero. Orthogonal wavelets yield stable, nonredundant expansions.
Scaling function: A function whose integer translates generate one level of a multiresolution approximation. Its refinement equation determines the associated wavelet's structure.

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