Wavelet de-noising of coarsely quantized signals

A methodology to address the problem of generating a de-noised estimate of a coarsely quantized, noise contaminated signal is presented via a two-step wavelet de-noising approach. In the first step, the signal is de-noised in accordance with the traditional wavelet de-noising methodologies, in which the noise contamination is assumed to be Gaussian. In the second step, a correction is then applied, through the use of a moving average signal estimate, to account for the non-Gaussian nature of the coarse quantization noise. This moving average signal estimate is also utilized in analyzing which combination of the tested mother wavelet functions, threshold determination methodologies, and thresholding functions provided the "best" estimate of the original noise-free signal. The motivation behind this work is to enable the development of model based fault detection approaches suitable for retro-fitting to existing industrial status monitoring systems.