A comparative study of noise effect on wavelet based de-noising methods

Complexity of noisy engineering or biological data often involves non-stationarity, non-gaussianity, long memory, self-similarity, multi-scale structure, etc. In application of wavelet based statistical methods to analyze these types of data it is of importance to know how the choice of wavelet basis function and the noise level contained in the signals affect the performance of a de-noising method applied to a set of multivariate noisy signals. In this paper, we study the performance of three wavelets based de-noising methods: wavelet thresholding, multivariate wavelet de-noising method and multi-scale principal component analysis (PCA), which are important wavelet based de-noising methods. We investigate the robustness of these methods to different types and levels of noise added to a set of known signals. We study the noise effect on de-noising performance using a set of signals with known structure for different types and levels of the added noise.