Instantaneous Frequency Estimation in Noisy Multicomponent Signals with Interfering Modes Based on Prony Method and Spline Approximation

In this paper, we propose a novel estimator of the instantaneous frequencies (IFs) of the modes making up multicomponent signals (MCSs). We are particularly interested in dealing with noisy MCSs containing close modes in the time-frequency plane. Though it is possible to adapt Prony approach to estimate IFs in such situations, interference between the modes generates oscillations in the obtained estimations. After having investigated the nature of these oscillations, we propose an algorithm to remove these in IFs estimation, based on spline approximation. Numerical applications in various situations illustrate the benefit of mixing Prony technique with spline approximation for IF estimation in noisy MCSs containing close modes.

Gridless 2D Recovery of Lines using the Sliding Frank-Wolfe Algorithm

We present a new approach leveraging the Sliding Frank--Wolfe algorithm to address the challenge of line recovery in degraded images. Building upon advances in conditional gradient methods for sparse inverse problems with differentiable measurement models, we propose two distinct models tailored for line detection tasks within the realm of blurred line deconvolution and ridge detection of linear chirps in spectrogram images.

Instantaneous Frequency Estimation in Multicomponent Signals in Case of Interference Based on the Prony Method

In this paper, we develop a general method to estimate the instantaneous frequencies of the modes making up a multicomponent signal when the former exhibit interference in the time-frequency plane. In particular, studying the representation given by the spectrogram, we show that it is possible to characterize the interference between the modes using the Prony method, which enables us to build a novel instantaneous frequency estimator for the mode. The relevance of the proposed approach is demonstrated by comparing it with different stateof-the art techniques based on ridge detection.