xi = si + ni,
corrupted by a zero mean white Gaussian noise ni (i = 1,…,N). Let W denote a N by N orthonormal wavelet transformation matrix. In the wavelet domain, the above equation can be expressed as
Xi = Si + Ni, or, X = S + N
with X = Wx, S = Ws, and N = Wn [5], [3].
Wavelet-domain filtering produces wavelet shrinkage estimates. That is, certain wavelet coefficients are reduced to zero. It has been shown that for a smooth function with additive Gaussian white noise of a specific energy level in a particular space of functions, there exists a theoretical threshold that completely removed the noise and successfully reproduced the original smooth function [6]. In general, the filter
H = diag[h(1), h(2),…,h(N)],
produces the signal estimate
[3].Thresholding is one method
of filtering.