Positive and negtive thresholding of scale multiplication

In hard thresholding to scale multiplication, it is believed that the signal multiscale product must be positive and the negative correlation between adjacent scales is produced by noise. However, there is still some negative signal correlation between adjacent scales. Here, this phenomenon is deeply analyzed in typical circumstances of two dimensions. On the ground of studying negative signal correlation, we apply two different thresholds to the positive and negative scale multiplication respectively to form a perfect bilateral thresholding scheme. These two thresholds are determined statistically to reduce most of the noise component. Experiments show that the proposed scheme outperforms the traditional thresholding scheme based on scale multiplication.