Wavelet shrinkage denoising by generalized threshold function

The wavelet shrinkage denoising method can effectively reduce the noise of non-stationary signal but preserve the local regularity. The central questions of wavelet shrinkage are how to choose threshold function and threshold value. In this paper, the generalized threshold function is build. Computationally exact formulas of bias, variance and risk of generalized threshold function are derived. On the basis of this, the relations between bias, variance a risk of generalized threshold function and threshold values, wavelet coefficients are compared. The Stein unbiased risk estimate (SURE) threshold value of generalized threshold function is derived. In end, the method is used to denoise the noisy phonocardiogram (PCG) signal; the result indicates that it has better denoising performance.