Prior knowledge and multiscaling in statistical estimation of signal-to-noise ratio - Application to deconvolution regularization

Abstract An improvement to the choice of the regularization parameter involved in a deconvolution procedure is proposed. It is based on a statistical model allowing a good estimation of the spectral signal-to-noise ratio. To this aim, first, a separation of signal and noise is performed through a multiresolution scheme, from the variance behavior of the wavelet coefficients of data as a function of resolution. Second, based on this separation, the autocorrelation functions of the signal and of the noise, and hence the spectral signal-to-noise ratio, are calculated with a probabilistic model incorporating the prior knowledge about the underlying physical phenomenon. This model is illustrated with a 1D example.