Blind frequency deconvolution : A new approach using mutual information rate

where d(t) is the recorded signal and n(t) is the additive sensor noise signal. Some methods (Champagnat et al., 1996; Lavielle, 1993) used in Bayesian formulation the prior hypothesis that the reflectivity signal r(t) is a Bernouilli-Gaussian process. The first step is a detection of the reflectors and it follows by a magnitude estimation. The high noise level on recordings limits the performance of the detection step. The deconvolution problem can be also applied to the seismovolcanic phenoma. Then, the recording is the result of a convolution between the excitation r(t) and the filter w, which is a resonant filter giving information about the volcano geometry. This data can be processed with a blind deconvolution algorithm, in whose only d(t) is accessible to the algorithm, whereas r, n and w are unknown parameters. In a blind deconvolution problem we aim at finding a deconvolution filter g for computing the output of deconvolution process y(t) = (g∗d)(t). Assuming the source signal r(t) is iid (Independently and Identically Distributed) and non Gaussian, the solution set of the blind deconvolution problem is generated by an only solution with a delay and magnitude modifications. Filter phase determination need to use higher order statistics (HOS). Boumahdi (Boumahdi, 1996) proposes to use the simplest HOS-the kurtosis-for estimating non-minimum phase Moving Average (MA) or autoregressive (AR) or ARMA models. These methods come up against the same problem of the noise. So, in the following part, we present our criterion and our algorithm using more general HOS, then in the last part we show tests about simulated and real data.