Bernoulli-Gaussian deconvolution in non-Gaussian noise from multiscale edges

Abstract

This paper deals with the problem of deconvolution of Bernoulli-Gaussian processes immerged in a non-Gaussian noise. We apply a wavelet decomposition to the process to gaussianise the noise and at each scale a classical detection-estimation algorithm is performed on the signal. Finally, we use a fusion strategy to merge all results and obtain the final deconvolved result. When the noise variance is available, its value can be used in the algorithm, performance is improved only for strongly non-Gaussian noise like Poisson noise. When the noise variance cannot be estimated, we show by simulation an improvement by our method.