Stéphane G. Mallat made some fundamental contributions to the development of wavelet

Wavelet

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...

 theory in the late 1980s and early 1990s. He has also done work in applied mathematics

Applied mathematics

Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...

, signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, music

Music

Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

 synthesis and image segmentation

Segmentation (image processing)

In computer vision, segmentation refers to the process of partitioning a digital image into multiple segments . The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze...

.

Specifically, he collaborated with Yves Meyer

Yves Meyer

Yves F. Meyer is a French mathematician and scientist and a foremost expert on wavelets.- Biography :Meyer was a professor at the Paris Dauphine University, at École Polytechnique and currently holds a position as Professor Emeritus at the École Normale Supérieure de Cachan.- Awards and...

 to develop the Multiresolution Analysis

Multiresolution analysis

A multiresolution analysis or multiscale approximation is the design method of most of the practically relevant discrete wavelet transforms and the justification for the algorithm of the fast wavelet transform...

 (MRA) construction for compactly supported wavelets, which made the implementation of wavelets practical for engineering

Engineering

Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

 applications by demonstrating the equivalence of wavelet bases

Basis (linear algebra)

In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system"...

 and conjugate mirror filters

Filter (signal processing)

In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...

 used in discrete

Discrete signal

A discrete signal or discrete-time signal is a time series consisting of a sequence of qualities...

, multirate filter bank

Filter bank

In signal processing, a filter bank is an array of band-pass filters that separates the input signal into multiple components, each one carrying a single frequency subband of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components...

s in signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

. He also developed (with Sifen Zhong) the Wavelet transform modulus maxima method for image characterization, a method that uses the local maxima of the wavelet coefficients at various scales to reconstruct images.

Mallat is the author of A Wavelet Tour of Signal Processing (ISBN 012466606X), a common text in some applied mathematics and engineering courses.

He has taught at New York University

New York University

New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...

, Massachusetts Institute of Technology

Massachusetts Institute of Technology

The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...

, Tel Aviv University

Tel Aviv University

Tel Aviv University is a public university located in Ramat Aviv, Tel Aviv, Israel. With nearly 30,000 students, TAU is Israel's largest university.-History:...

and currently at the École polytechnique

École Polytechnique

The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...

.

External links

• Home page at École polytechnique
  École Polytechnique
  The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...