Wavelets

Level SpecializationDifficulty ★★★★★Concept⌖ Open in the map

What is it?

Localized oscillations at several scales: unlike sines, they say when a frequency occurs. Multiresolution analysis underlies JPEG 2000, denoising and some feature extractors.

Formulas

\psi_{a,b}(t) = \frac{1}{\sqrt{|a|}}\,\psi\Big(\frac{t - b}{a}\Big)

Where it shows up in computing

Media compression (JPEG, MP3, video)★★★★★frequentSignals, media and vision
JPEG 2000 and many medical/scientific image formats use wavelet transforms.
Image processing and computer vision★★★★★frequentSignals, media and vision
Wavelet shrinkage is a classic denoising method.

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

∿ Signals, media and vision

Media compression (JPEG, MP3, video)★★★★★
Image processing and computer vision★★★★★

This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.