Noiselet

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 conversely. 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 conversely. 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. MRI data can be acquired in noiselet domain, and, subsequently, images can be reconstructed from undersampled data using compressive-sensing reconstruction.