Full frequency de-noising method based on wavelet decomposition and noise-type detection

Traditional wavelet threshold de-noising techniques assume that noise is spread over a high frequency band of signal. However, it may not be true for some noise, and those methods rarely concern the noise in low frequency bands. This motivates us to study new methods to reduce noise in the whole wavelet frequency band. Thus, a new framework named Full Frequency band De-noising based on Noise-type Detection (FFD-ND) is proposed. In this framework, a noise type is detected by analyzing autocorrelation coefficients for different noise, and then noise reduction is performed both in low and high frequency band by using different thresholds for different noise models. To analyze the necessity for de-noising in low frequency bands, we firstly study the relationships between power spectral densities (PSDs) and wavelet decomposition scales for some noisy models, and find that it is not true for most of the noises and that PSDs decline with the reduction of wavelet decomposition scales. As for wavelet threshold value, we also find that it relies not only on wavelet decomposition scales but also on noise models. To adaptively determine the threshold value, we then propose an adaptive approach, in which the threshold value is functionally dependent on noise model, wavelet decomposition layers and other factors. The proposed approach can always achieve better performance with lower computation cost and fewer decomposition scales than a high frequency de-noising method. We also experimentally verify that the performance of our method for noise-type detection is super than the methods based on neural network.