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 ne ...

and

École normale supérieure 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 flowing in région Île-de-France * École, Savoi ...

. 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 mathematical s ...

signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniq ...

music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

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 s ...

, 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 introd ...

(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 tha ...

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 bank In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency Sub-band coding, sub-band of the original signal. One application of ...

s in

. He also developed (with Sifen Zhong) the

wavelet transform modulus maxima method The wavelet transform modulus maxima (WTMM) is a method for detecting the fractal dimension of a signal. More than this, the WTMM is capable of partitioning the time and scale domain of a signal into fractal dimension regions, and the method is so ...

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, the ...

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

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 flowing in région Île-de-France * École, Savoi ...

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 page
at

* {{DEFAULTSORT:Mallat, Stephane 20th-century French mathematicians 21st-century French mathematicians Scientists from Paris Living people 1962 births