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Noiselets are a family of functions which are related to wavelets, analogously to the way that the Fourier basis is related to a time domain 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.[1]


The complementarity of wavelets and noiselets means that noiselets can be used in compressed sensing to reconstruct a signal (such as an image) which has a compact representation in wavelets.[2]


  1. ^ R. Coifman, F. Geshwind, and Y. Meyer, Noiselets, Applied and Computational Harmonic Analysis, 10 (2001), pp. 27–44. doi:10.1006/acha.2000.0313
  2. ^ E. Candes and J. Romberg, Sparsity and incoherence in compressive sampling, 23 (2007), pp. 969-985. doi:10.1088/0266-5611/23/3/008