On the incoherence of noiselet and Haar bases

Tomas Tuma (1) , Paul Hurley (1)

1 IBM Zurich Research Laboratory

Noiselets are a family of functions completely uncompressible using Haar wavelet analysis. The resultant perfect incoherence to the Haar transform, coupled with the existence of a fast transform has resulted in their interest and use as a sampling basis in compressive sampling. We derive a recursive construction of noiselet matrices and give a short matrix-based proof of the incoherence.

Domaines: Analyse classique [math.CA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Tomas Tuma, Paul Hurley. On the incoherence of noiselet and Haar bases. SAMPTA'09, May 2009, Marseille, France. pp.General session. ⟨hal-00453288⟩