Smoothing non-uniform data samples with wavelets
Kevin Wheeler · 1997
This thesis presents a data smoothing method for reducing noise in non-uniformly sampled data. The method relies on a threshold found via cross-validation applied to a wavelet decomposition. Standard wavelet transforms require data to be uniformly sampled. Second generation wavelets allow for decomposition of non-uniformly spaced samples. Lifting is a method for increasing the number of vanishing moments of the wavelet functions. This lifting process may be used as a basis selection method. Noisy data may be smoothed by performing a wavelet transformation, thresholding the coefficients, and then performing an inverse transformation. In this thesis, second generation wavelets and lifting have been combined with thresholding to smooth non-uniformly sampled data with noise of an unknown distribution. The proper threshold value was determined via cross-validation. The results of this data smoothing method were compared with similar techniques such as smoothing splines, radial basis function neural networks, and other wavelet thresholding techniques.