Mt department Nazirova E. Sh

Wavelet denoising Suppose we measure a noisy signal . Assume s has a sparse representation in a certain wavelet bases, and So:

Most elements in p are 0 or close to 0, and .

Since W is orthogonal, the estimation problem amounts to recovery of a signal in iid Gaussian noise. As p is sparse, one method is to apply a Gaussian mixture model for p.



Figure 1.7 Signal denoising by wavelet transform thresholding

Assume a prior is the variance of "significant" coefficients, and is the variance of "insignificant" coefficients.

Then is called the shrinkage factor, which depends on the prior variances and The effect of the shrinkage factor is that small coefficients are set early to 0, and large coefficients are unaltered. Small coefficients are mostly noises, and large coefficients contain actual signal. At last, apply the inverse wavelet transform to obtain