VIBRATION IMPULSES DENOISING BASED ON A BAYESIAN APPROACH AND SIGNAL SPARSITY ENHANCEMENT

摘要

The problem of removing Gaussian noise from vibration signals is an interesting inverse problem to be investigated in this paper through a sparse representation. The sparsity is a property which can be described either directly for the signal itself or after some transformation. In this work, the sparsity is considered on the noisy coefficients in wavelet basis in which, the observations are sparsely represented. Wavelet decomposition is performed using an optimal Morlet wavelet function. To enforce the sparsity, a strongly non-Gaussian probabilistic density is considered to model the prior of the corresponding wavelet coefficients. In probabilistic terms, the prior corresponds to a density function with a marked peak at zero and heavy tails. The Bayesian computations are based on optimizing the maximum a posteriori (MAP) estimator. The present method shows how the Bayesian approach can provide an efficient way for translating the prior knowledge and in particular the sparsity and gives an in-depth analysis of the inspected signal even at very low signal to noise ratio (SNR).