Bernoulli-Gaussian deconvolution in non-Gaussian noise, contribution of wavelet decomposition

We introduce a method to restore Bernoulli-Gaussian processes immerged in a non-gaussian noise. It uses wavelet decomposition to "gaussianize" the noise. The convergence, after wavelet projection, of some non-gaussian noise to a gaussian noise quantifies the quality of the "gaussianization" effect of the wavelet. This property is used to apply a Bernoulli-Gaussian algorithm at each scale of wavelet decomposition. After, we use a fusion strategy to merge all results. We obtain also a new deconvolution algorithm which is very performant, for all satistical noises, when the noise variance is not well estimated. When the noise variance is correctly estimated, it improves the classical Bernoulli-Gaussian algorithm for strongly non-Gaussian noises.