A Novel Pseudo-Bayesian Approach for Robust Multi-Ridge Detection and Mode Retrieval

Abstract

This paper introduces a novel approach for extracting the elementary components present in an observed nonstationary mixture signal. Our technique based on a pseudo-Bayesian approach operates in the time-frequency plane and sequentially estimates the ridge of each component that is required for mode extraction. We compare our results with those obtained with the state-of-the-art Brevdo method which has shown its efficiency for disentangling multicomponent noisy signals. Our results reveal an improvement of the reconstruction performance when compared to the state of the art.

Pseudo-Bayesian Approach for Robust Mode Detection and Extraction Based on the STFT

“…Moreover, a novel objective function is introduced to regularize the estimation process according to both the presence of multiple ridges or a strong noise level involving possible model mismatch. This generalizes and extends our previous contribution [ 20 ], which only addressed one of these two constraints separately by respectively minimizing a divergence enforcing either the robustness or the mass-covering character of the variational approximation [ 21 ]. More precisely, an Alpha-Beta (AB) variational objective [ 21 , 22 ] is used to obtain a more general control over the inference process.…”

“…The variational objective can be modified to account for the lack of accuracy of the postulated model by replacing the KLD used in the first term of Equtaion ( 8 ) by another divergence. In [ 20 ], both the -Divergence ( -D) and the -Divergence ( -D) were proposed, providing, respectively, robustness of the estimates and a control over the mass-covering behavior of the variational approximation.…”

“…We aim to compare the performance of our algorithm to several state-of-the-art methods [ 11 , 20 , 33 ] on synthetic data for a first time. For this purpose, we consider a signal made of three components corresponding to a sinusoidal (C1), a linear chirp (C2) and a sinusoidally-FM component (C3) depicted in Figure 4 (from bottom to top).…”

“…Using provides the best accuracy at high SNR by using the compared variational objectives of the proposed method while at low SNR we obtain estimation performance similar to the -D and the -D. Finally, the robust approach using is mainly efficient at low SNR where it provides the best performances among the competing methods. It can be remarked that our most robust approach, , reaches better performance than when using the -D with [ 20 ].…”

“…We assess the performance of the detection method through a comparison with [ 20 , 33 ] using the following Mean Absolute Error (MAE) defined as where (resp. ) is the actual (resp.…”