Signal waveform restoration by wavelet denoising

In this paper, we first establish an approximated sampling theorem for an arbitrary continuous signal which is essential for wavelet analysis. The differences and similarities between quadrature mirror filter decomposition and wavelet decomposition are contrasted. We then propose an efficient way to recover a source signal buried in white noise by using wavelet denoising. The method is capable of reducing the mean square error bound from O(log/sup 2/(n)) to O(log(n)), where n is the number of samples. It is also shown that the new estimator is asymptotically unbiased if the source signal is a piece-wise polynomial.