Comparison and Assessment of Various Wavelet and Wavelet Packet based Denoising Algorithms for Noisy Data

Denoising of measured data is an important method in data analysis and of great significance in many industrial applications. For example pattern recognition often needs signal denoising as a kind of preprocessing, followed by the actual classification. Denoising of measured data can be seen as a problem in nonparametric regression where an unknown function f has to be revealed from a signal f̃ containing undesired overlaying noise ξ. In the following we assume that noisy empirical data f̃i are measured at equidistant points ti ∈ [a, b] and f̃i results from a superposition of f at point ti with white noise ξi of variance σ .