Estimating a signal embedded in noise requires taking advantage of any prior information about the signal and noise. Until recently, signal processing estimation was primarily Bayesian and linear. Non-linear smoothing algorithms existed in statistics, but these procedures were often ad-hoc and complex. Donoho and Johnstone proved that a simple thresholding algorithm on an appropriate basis could be a nearly optimal non-linear estimator.
A radio signal induced from cosmic ray is very well described, for example, by the Daubechies wavelets as a basis, allowing the thresholding to be as safe (or more) as a linear estimation. The best basis search or a pursuit algorithm may also improve the thresholding performance as it adapts the basis to the noisy data.
This work presents the wavelets as a denoising technique for narrowband and gaussian background reduction in radio signals induced from cosmic rays, showing its efficiency in energy reconstruction.