The term noiselet refers to a family of functions which are related to wavelet

Wavelet

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...

s, analogously to the way that the Fourier basis

Basis function

In mathematics, a basis function is an element of a particular basis for a function space. Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis...

 is related to a time domain

Time domain

Time domain is a term used to describe the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various...

 signal. In other words, if a signal is compact in the wavelet domain then it will be spread out in the noiselet domain, and vice versa.

Applications

The complementarity of wavelets and noiselets means that noiselets can be used in compressed sensing

Compressed sensing

Compressed sensing, also known as compressive sensing, compressive sampling and sparse sampling, is a technique for finding sparse solutions to underdetermined linear systems...

to reconstruct a signal (such as an image) which has a compact representation in wavelets.