A new frame based de-noising procedure for fast oscillating signals

In recent years there has been a growing interest in frame based de-noising procedures. The advantage of frames with respect to classical orthonor- mal bases (e.g. wavelet, Fourier, polynomial) is that they can furnish an efficient representation of a more broad class of signals. For example, signals which have fast oscillating behavior as sonar, radar, EEG, stock market, audio and speech are much more well represented by a frame (with similar oscillating characteristic) than by a classical wavelet basis, although the frame representation for such kind of signals can be not properly sparse. In literature the frame based de-noising procedures can be divided into two classes: Bayesian approaches and variational approaches: both types promote sparseness through specific prior hypothesis or penalization term. A new frame based de-noising procedure is presented where no sparseness hypothesis is required on frame coefficients. In particular, the estimator is derived as the empirical version of the Wiener filter general- ized to the frame operator. An analytic expression of it is furnished so no searching strategy is required for the implementation. Results on standard and real test signals are presented.