Signal De-Noising by Improving Soft Thresholding on the Dyadic Wavelet Transform
Soft thresholding method has been a standard procedure in signal de-noising. Theoretically, it is also almost optimal in the sense of minimax mean-squared error. This paper shows that by combining coefficient de-noising and soft thresholding, a lower bound of mean-squared-error can be achieved. Furthermore, the translation-invariant (TI) dyadic wavelet transform is used instead of DWT, which can avoid the artifacts caused by the non-TI reconstruction. Experiments show that the proposed method improves the signal-to-noise ratios of the de-noised signals. Moreover, the de-noised signals have smooth and nice visual appearance.