Stéphane Georges Mallat (born 24 October 1962) is a French applied mathematician, concurrently appointed as Professor at

Collège de France The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...

and

École normale supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...

. 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 n ...

theory in the late 1980s and early 1990s. He has additionally done work in

applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

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, Scalar potential, potential fields, Seismic tomograph ...

music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

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 (Set (mathematics), sets of pixels). The goal of segmen ...

. With 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 int ...

(MRA) construction for compactly supported wavelets. His MRA wavelet construction made the implementation of wavelets practical for

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

applications by demonstrating the equivalence of wavelet bases and conjugate mirror

filters Filtration is a physical process that separates solid matter and fluid from a mixture. Filter, filtering, filters or filtration may also refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Fil ...

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, ...

, 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 sub-band of the original signal. One application of a filter bank is a graphic equal ...

s in

. 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 university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

École polytechnique (, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mat ...

and at the Ecole normale supérieure. He is currently Professor of Data Science at

College de France A college (Latin: ''collegium'') may be a tertiary education, tertiary educational institution (sometimes awarding academic degree, degrees), part of a collegiate university, an institution offering vocational education, a further educatio ...

. 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 IMU Abacus Medal (known before ...

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