Time-Frequency Ridge Estimation of Multi-Component Signals using Sparse Modeling of Signal Innovation

Abstract: This paper presents a novel approach for estimating the modes of an observed non-stationary mixture signal. A link is first established between the short-time Fourier transform and the sparse sampling theory, where the observations are modeled as a stream of pulses filtered by a known function. As the signal to retrieve has a finite rate of innovation (FRI), an adapted reconstruction approach is used to estimate the signal modes in the presence of noise. We compare our results with state-of-the-art methods and validate our approach by highlighting an improvement of the estimation performance in different scenarios. Our approach paves the way of future FRI-based mode disentangling algorithms.