Localized denoising filtering using the wavelet transform

Gravity and magnetic signals are usually affected by noise, which is in turn related either to the geological heterogeneity of the shallow structures or to the measurement and data processing procedures. Along the map, the signal is represented by field anomalies which overlap with the noise in a variable and complicated way. Classical filtering techniques such as the Fourier (band-pass) filtering or the wavelet "cycle-spinning" method denoise the data only in a global sense and are therefore inaccurate when the frequency content of the signal is no longer uniform. We propose instead a localized denoising of such data, based on localized filtering techniques using the wavelet transform. The localized denoising filtering is based on a "soft thresholding" rule and is characterized by a local thresholding parameter (LTP). An adaptive tuning of the LTP parameter allows enhancement of the high frequencies of the signal and is effective to remove the noise as much as possible. The method is confronted using two different kinds of wavelets, namely the biorthogonal and the multiscale shiftable transforms and is applied to the noisy Vertical derivative of the gravity field of Sicily. The technique proves to be superior to classical methods and may be similarly applied to any manner of geophysical data.