Stéphane Georges Mallat (born 24 October 1962) is a French applied mathematician, concurrently appointed as Professor at
Collège de France
The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment ('' grand établissement'') in France. It is located in Paris ...
and
École normale supérieure
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education
Secondary education or post-primary education covers two phases on the International Standard Classification of Education sca ...
. He made fundamental contributions to the development of
wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ...
theory in the late 1980s and early 1990s. He has additionally done work in
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemat ...
,
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
,
music
Music is generally defined as the The arts, art of arranging sound to create some combination of Musical form, form, harmony, melody, rhythm or otherwise Musical expression, expressive content. Exact definition of music, definitions of mu ...
synthesis and
image segmentation
In digital image processing and computer vision, image segmentation is the process of partitioning a digital image into multiple image segments, also known as image regions or image objects ( sets of pixels). The goal of segmentation is to simpl ...
.
With
Yves Meyer
Yves F. Meyer (; born 19 July 1939) is a French mathematician. He is among the progenitors of wavelet theory, having proposed the Meyer wavelet. Meyer was awarded the Abel Prize in 2017.
Biography
Born in Paris to a Jewish family, Yves Meyer ...
, he developed the
multiresolution analysis
A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms (DWT) and the justification for the algorithm of the fast wavelet transform (FWT). It was intr ...
(MRA) construction for compactly supported wavelets. His MRA wavelet construction made the implementation of wavelets practical for
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
applications by demonstrating the equivalence of wavelet
bases and conjugate mirror
filters
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component th ...
used in
discrete
Discrete may refer to:
*Discrete particle or quantum in physics, for example in quantum theory
*Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit
*Discrete group, a ...
, multirate
filter banks in
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
. 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.
He introduced the scattering transform that constructs invariance for object recognition purposes. Mallat is the author of ''A Wavelet Tour of Signal Processing'' (1999; ), a text widely used in applied mathematics and engineering courses.
He has held teaching positions at
New York University
New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then- Secretary of the Treasury Albert Gallatin.
In 1832, ...
,
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...
,
École polytechnique
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine
The Seine ( , ) is a river in northern Franc ...
and at the
Ecole normale supérieure. He is currently Professor of Data Science at
College de France
A college (Latin: ''collegium'') is an educational institution or a constituent part of one. A college may be a degree-awarding tertiary educational institution, a part of a collegiate or federal university, an institution offering v ...
.
In 1998 he was a plenary speaker at the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
in Berlin.
Publications
* A wavelet tour of signal processing: the sparse way, Academic Press, 1998, 3rd edn. 2009
*
*
*
References
External links
Home pageat
École normale supérieure
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education
Secondary education or post-primary education covers two phases on the International Standard Classification of Education sca ...
Home pageat
College de France
A college (Latin: ''collegium'') is an educational institution or a constituent part of one. A college may be a degree-awarding tertiary educational institution, a part of a collegiate or federal university, an institution offering v ...
*
{{DEFAULTSORT:Mallat, Stephane
20th-century French mathematicians
21st-century French mathematicians
Scientists from Paris
Living people
1962 births