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WonderApplied mathematics biography

In 1988 Belgian-American mathematician Ingrid Daubechies published the wavelets now named after her: small wave-like patterns that split a signal into its broad outline and its fine detail. Wavelets like hers help compress images, clean up noisy data and store fingerprints.

Ingrid Daubechies

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Fourier analysis, the classic tool for signals, shows which frequencies a sound or picture contains but not where they occur. Wavelets can also show where a sudden change or sharp edge happens. Working at the Courant Institute in New York in 1986–87, Daubechies found wavelets that are exact, confined to a short stretch of the signal and quick to compute, which let wavelets move from theory into everyday digital processing. Related wavelets she co-designed are used in the JPEG 2000 image standard, and the FBI's fingerprint archive relies on wavelet compression. She has also used these methods to study paintings by Van Gogh and to support the restoration of the Ghent Altarpiece. In 2011 she became the first woman to lead the International Mathematical Union, and in 2023 the first woman to win the Wolf Prize in Mathematics.

Türkçe oku
Belçika asıllı Amerikalı matematikçi Ingrid Daubechies, bugün adıyla anılan dalgacıkları 1988'de yayımladı. Dalgacıklar bir sinyali kaba hatlarına ve ince ayrıntılarına ayıran küçük dalga biçimleridir; görüntü sıkıştırmada, gürültülü verilerin temizlenmesinde ve parmak izlerinin saklanmasında kullanılır.

Sinyal incelemenin klasik aracı Fourier analizi, bir seste ya da görüntüde hangi frekansların bulunduğunu söyler ama bunların nerede ortaya çıktığını göstermez. Dalgacıklar ise ani bir değişimin ya da keskin bir kenarın yerini de verir. Daubechies 1986–1987'de New York'taki Courant Enstitüsü'nde çalışırken kesin sonuç veren, sinyalin yalnızca kısa bir bölümünü kapsayan ve hızla hesaplanabilen dalgacıklar buldu. Böylece dalgacıklar kuramdan çıkıp gündelik sayısal işlemlere girdi. Ortak geliştirdiği benzer dalgacıklar JPEG 2000 görüntü standardında kullanılıyor; FBI'ın parmak izi arşivi de dalgacıklarla sıkıştırılıyor. Daubechies bu yöntemlerle Van Gogh tablolarını da inceledi ve Gent Sunağı'nın restorasyonuna katkıda bulundu. 2011'de Uluslararası Matematik Birliği'nin başına geçen ilk kadın, 2023'te de Wolf Matematik Ödülü'nü alan ilk kadın oldu.

Sources and further reading

Background reading: Ingrid Daubechies
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