Wavelet modulation, and recovery of weak signals via frequency selective thresholding

摘要

The limitations of straight forward wavelet transformations have been investigated for some time. In this paper, it is shown that the time-frequency resolution tradeoff may be significantly improved by frequency modulating the mother wavelet. In this way weak signal components may be more efficiently recovered from strong noise. This technique is applied on discrete seismic data sets. In addition to frequency modulating the mother wavelet, it is shown that the quality of the recovered signals may be substantially improved by the application of weights to modify the mean wavelet transform of the data set. The two-dimensional variance and signal-to-noise ratio (SNR) plots will be used in order to achieve this goal. It is also shown that by employing a frequency selective thresholding method, even better results as far as suppressing noise while keeping the signal can be attained.