This paper puts forward a generalization of the short-time Fourier-based synchrosqueezing transform using a new local estimate of instantaneous frequency. Such a technique enables not only to achieve a highly concentrated time-frequency representation for a wide variety of amplitude- and frequency-modulated multicomponent signals but also to reconstruct their modes with a high accuracy. Numerical investigation on synthetic and gravitational-wave signals shows the efficiency of this new approach.

In this paper, we present a novel technique for the retrieval of the modes of a multicomponent signal using a time-frequency (TF) representation of the signal. Our approach is based on a novel ridge extraction method that takes into account the fact that the TF representation is both discrete in time and frequency, followed by a demodulation procedure. Numerical results show the benefits of the proposed approach for mode reconstruction in comparison to similar techniques that do not make use of demodulation. Furthermore, numerical investigations show that the proposed approach sharpens the TF representation on which it is built.

The general aim of this paper is to introduce the concept of synchrosqueezing transforms (SSTs) that was developed to sharpen linear time–frequency representations (TFRs), like the short-time Fourier or the continuous wavelet transforms, in such a way that the sharpened transforms remain invertible. This property is of paramount importance when one seeks to recover the modes of a multicomponent signal (MCS), corresponding to the superimposition of AM/FM modes, a model often used in many practical situations. After having recalled the basic principles of SST and explained why, when applied to an MCS, it works well only when the modes making up the signal are slightly modulated, we focus on how to circumvent this limitation. We then give illustrations in practical situations either associated with gravitational wave signals or modes with fast oscillating frequencies and discuss how SST can be used in conjunction with a demodulation operator, extending existing results in that matter. Finally, we list a series of different perspectives showing the interest of SST for the signal processing community.

This letter deals with the problem of the estimation of the instantaneous frequencies of the modes of multicomponent signals from their linear time-frequency representations. In most approaches, such an estimation consists of extracting the ridges associated with each mode in the time-frequency plane. A major issue associated with these techniques is that ridge detection relies on some ad-hoc parameters, which essentially bound the modulation of the studied modes and put some constraints on the type of filter used in the time-frequency representation. In this paper, we alternatively propose a novel fully adaptive approach for ridge detection whose relevance is shown throughout numerical simulations.

This article addresses the problem of high-resolution Doppler blood flow estimation from an ultrafast sequence of ultrasound images. Formulating the separation of clutter and blood components as an inverse problem has been shown in the literature to be a good alternative to spatio-temporal singular value decomposition (SVD)-based clutter filtering. In particular, a deconvolution step has recently been embedded in such a problem to mitigate the influence of the point spread function (PSF) of the imaging system. Deconvolution was shown in this context to improve the accuracy of the blood flow reconstruction. However, the PSF needs to be measured experimentally, and measuring it requires nontrivial experimental setups. To overcome this limitation, we propose herein a blind deconvolution method able to estimate both the blood component and the PSF from Doppler data. Numerical experiments conducted on simulated and in vivo data demonstrate qualitatively and quantitatively the effectiveness of the proposed approach in comparison with the previous method based on experimentally measured PSF and two other state-of-the-art approaches.