The localization of interference associated with crossing modes in thetime-frequency(TF) plane is of significant interest when the objective is to separate these modes. Prior to localizing mode crossings, it is essential to determine whether the observed interference arises from closely spaced modes or from actual mode crossings. In this paper, we propose a novel technique to discriminate between these different types of interference in the TF plane and to subsequently localize mode crossings. The proposed approach exhibits strong adaptability across a wide range of scenarios and demonstrates robustness to noise, as confirmed by simulation results.

This paper aims at building a new instantaneous frequency (IF) estimator of the modes making up non-stationary multi-component signals, using reassignment operators used in Fourier-based synchrosqueezing transforms (FSSTs) and linear chirp points detection. Reassignment operators provide with different IF estimates, depending on the assumption made on the local polynomial order of the phase of the studied mode. In practice, it is difficult to estimate locally which order fits the best, and to choose too high an order, typically larger than two, when not necessary results in both an inaccurate estimation and an increased sensitivity to noise. To circumvent this, we propose to localize linear chirp points in modes to find out where second order phase approximation is sufficient for the estimation, and then build a new IF estimate based on a weighted spline approximation based on these points. Numerical results show the improvement brought by the proposed approach in noisy situations over classical IF estimators used in FSSTs.

In this work, we explore the problem of making synchrosqueezing transform adaptive. To deal with multicomponent signals, existing methods use a fixed order N, thus assuming all the modes making up the signal have order N polynomial phases. To go beyond this limitation, we introduce a new criterion based on the concentration of the representation to locally choose the best order for the synchrosqueezing transform. We study the performance of the proposed approach in terms of the error with respect to the ideal time-frequency representation, both on synthetic and real signals.

In this paper, we propose a novel approach to classify the spectrogram zeros (SZs) of multicomponent signals based on the analysis of the Voronoï cells associated with these zeros. More precisely, the characterization of the distribution of the spectrogram maxima of a complex white Gaussian noise along the edges of the Voronoï cells associated with SZs enables us to derive an algorithm to classify the different types of zeros present in the spectrogram of a multicomponent signal. Numerical applications on simulated signals confirm the relevance of the proposed classification algorithm, and an illustration on a real signal concludes the paper.

In this paper, we investigate the conditions for the separation of two pure tones from the spectrogram computed with a Gaussian window. For this purpose, we put forward necessary and sufficient conditions for the existence of spectrogram ridges associated with each signal. We then show how this condition easily extends to the case of parallel linear chirps, i.e., signals with constant amplitude, linear instantaneous frequency, and same chirp rate.

In this article, we present a new algorithm for fast, online 3D reconstruction of dynamic scenes using times of arrival of photons recorded by single-photon detector arrays. One of the main challenges in 3D imaging using single-photon lidar in practical applications is the presence of strong ambient illumination which corrupts the data and can jeopardize the detection of peaks/surface in the signals. This background noise not only complicates the observation model classically used for 3D reconstruction but also the estimation procedure which requires iterative methods. In this work, we consider a new similarity measure for robust depth estimation, which allows us to use a simple observation model and a non-iterative estimation procedure while being robust to mis-specification of the background illumination model. This choice leads to a computationally attractive depth estimation procedure without significant degradation of the reconstruction performance. This new depth estimation procedure is coupled with a spatio-temporal model to capture the natural correlation between neighboring pixels and successive frames for dynamic scene analysis. The resulting online inference process is scalable and well suited for parallel implementation. The benefits of the proposed method are demonstrated through a series of experiments conducted with simulated and real single-photon lidar videos, allowing the analysis of dynamic scenes at 325 m observed under extreme ambient illumination conditions.

In this paper, we investigate the determination of an optimal window length associated with the computation of the short time Fourier transform of multicomponent signals. In recent years the Rényi entropy has been widely used for that purpose, but the understanding of the significance of the obtained minimum in relation with the studied signal is still partial. In this paper, we explain in what way the window minimizing the Rényi entropy reflects the modulation of the modes making up the signal, and in which circumstances to use such a window is actually relevant.

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.

In this paper, we introduce a novel time-frequency technique for the retrieval of the modes of multicomponent signals based on linear chirp approximation. The key idea to this new technique is to design the retrieval procedure by using only information extracted in the vicinity of the ridges made by the components in the time-frequency plane. Compared with state-of-the-art methods based on time-frequency representations, the proposed approach will prove to improve the reconstruction results when applied to a monocomponent signal and to circumvent the mode-mixing issue when the modes of a multicomponent signal are close in the time-frequency plane.

The modulus of time-frequency representations, like the short-time Fourier or wavelet transforms, of a multicomponent signal exhibit ridges from which one usually computes estimations of the instantaneous frequencies of the modes making up the signal. But, due to the finite frequency resolution, the estimations thus obtained are piecewise constant. Our aim in this letter is to introduce a novel method for the estimation of the instantaneous frequencies of the modes based on the modeling of the modulus of the short-time Fourier transform, and then to propose a novel technique for mode retrieval. Numerical experiments carried out on both simulated and real signals demonstrate the benefits of the proposed approach over others based on the short-time Fourier transform.

This paper addresses the issues of the denoising and retrieval of the components of multicomponent signals from their short-time Fourier transform (STFT). After having recalled the hard-thresholding technique, in the STFT context, we develop a new thresholding technique by exploiting some limitations of the former. Numerical experiments illustrating the benefits of the proposed method to retrieve the modes of noisy multicomponent signals conclude the paper.

This letter introduces a new technique for phonocardiogram (PCG) signal denoising based on nonnegative matrix factorization (NMF) of its spectrogram and adaptive contour representation computation (ACRC) of its short-time Fourier transform (STFT). More precisely, NMFs on PCG and synchronous electrocardiogram spectrograms are first used to filter out high-energy noises from PCG. Then, ACRC is performed on a low-pass filtered version of the STFT of the resulting signal to identify relevant time-frequency components that are subsequently used for signal retrieval. Numerical experiments conducted on a real database of noisy PCG signals, Signal Separation Evaluation Campaign (SiSEC2016), illustrate the superiority of the proposed method over state-of-the-art techniques.

In this paper, we consider ridge detection for multicomponent signal analysis. We introduce a new ridge detector based on a projection of the reassignment vector in a specific direction which is related to the geometry of the spectrogram magnitude. The ridge definition we introduce enables that of the basin of attraction associated with a ridge and then mode reconstruction. Simulations show better concentration of the information on the ridges obtained by our method compared to other existing ridge detectors that also make use of the reassignment vector.

The paper deals with the problem of representing non-stationary signals jointly in time and frequency. We use the framework of reassignment methods, that achieve sharp and compact representations. More precisely, we introduce an enhanced version of the synchrosqueezed wavelet transform, which is shown to be more general than the standard synchrosqueezing, while remaining invertible. Numerical experiments measure the improvement brought about by using our new technique on synthetic data, while an analysis of the gravitational wave signal recently observed through the LIGO interferometer applies the method on a real dataset.

This letter introduces new chirp rate and instantaneous frequency estimators designed for frequency-modulated signals. These estimators are first investigated from a deterministic point of view, then compared together in terms of statistical efficiency. They are also used to design new recursive versions of the vertically synchrosqueezed short-time Fourier transform, using a previously published method (D. Fourer, F. Auger, and P. Flandrin, “Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., Mar. 2016, pp. 4880-4884). This study paves the way to the real-time computation of a time-frequency representation, which is both invertible and sharply localized in frequency.

This letter addresses the problem of the detection and estimation of the modes of a multicomponent signal using the reassignment framework. More precisely, we propose a new algorithm to estimate the ridges representing the time-frequency signatures of the modes based on the local orientation of the reassignment vector, and use them to define the so-called basins of attraction enabling modes' retrieval. Compared with previous approaches, this new technique not only enables reconstruction of AM/FM modes but also Dirac impulses, which is of great interest in many practical situations. Numerical experiments conducted with both synthetic and real data illustrate the effectiveness of the technique.

In this paper, we propose to improve the classical lifting-based wavelet transforms by defining three classes of pixels which will be predicted differently. More specifically, the proposed idea is inspired by the Essentially Non-Oscillatory (ENO) transform and consists in shifting the stencil used for prediction in order to reduce the error near image singularities. Moreover, the different filters associated with these classes will be optimized in order to design a multiresolution representation well adapted to image characteristics. Our simulations show that the resulting multiscale representation leads to much lower amplitudes of the detail coefficients and improves the linear approximation properties.

The aim of this paper is to construct a new nonlinear and nonseparable multiscale representation of piecewise continuous bidimensional functions. This representation is based on the definition of a linear projection and a nonlinear prediction operator, which locally adapts to the function to be represented. This adaptivity of the prediction operator proves to be very interesting for image encoding in that it enables a considerable reduction in the number of significant coefficients compared with other representations. Applications of this new nonlinear multiscale representation to image compression and super-resolution conclude this paper.

The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are extensively used to analyze and process multicomponent signals, i.e. superpositions of modulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relation inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the CWT, it provides a sharp, concentrated representation, while remaining invertible. This technique received a renewed interest with the recent publication of an approximation result related to the application of the synchrosqueezing to multi-component signals. In the current paper, we adapt the formulation of the synchrosqueezing to the STFT and state a similar theoretical result to that obtained in the CWT framework. The emphasis is put on the differences with the CWT-based synchrosqueezing with numerical experiments illustrating our statements.

This paper addresses the issue of the retrieval of the components of a multicomponent signal from its short-time Fourier transform. It recalls two popular reconstruction methods, and extends each of them for the case of strong frequency modulation, by taking into account the second derivative of the phase. Numerical experiments illustrate the improvement and compare the methods.

In this letter, we propose a novel approach to blob detection based on wavelet transform modulus maxima. We use maxima lines in scale-space to build a new blob detector. The algorithm we propose enables automatic blob detection and blob size determination. The robustness to noise of the blob detector we propose is also shown

The empirical mode decomposition (EMD) is an algorithmic construction that aims at decomposing a signal into several modes called intrinsic mode functions. In this letter, we present a new approach for the EMD based on the direct construction of the mean envelope of the signal. The definition of the mean envelope is achieved through the resolution of a quadratic programming problem with equality and inequality constraints. Some numerical experiments conclude this letter, and comparisons are carried out with the classical EMD.

In this correspondence, we propose a new approach to scale-space filtering using a box spline representation of multidimensional signals. The use of box splines is motivated by their ability to handle complex geometries better than tensor-product B-splines. The box spline we use is defined by a set of vectors invariant under the multiplication by a sampling matrix. We show that such a box spline satisfies a dilation equation which is the basis for the scale-space filtering we propose. Several numerical applications in 2-D conclude the correspondence.

The modeling of sample distributions with generalized Gaussian density (GGD) has received a lot of interest. Most papers justify the existence of GGD parameters through the asymptotic behavior of some mathematical expressions (i.e., the sample is supposed to be large). In this paper, we show that the computation of GGD parameters on small samples is not the same as on larger ones. In a maximum likelihood framework, we exhibit a necessary and sufficient Condition for the existence of the parameters. We derive an algorithm to compute them and then compare it to some existing methods on random images of different sizes.

In this letter, we describe a new method for bidimensional empirical mode decomposition (EMD). This decomposition is based on Delaunay triangulation and on piecewise cubic polynomial interpolation. Particular attention is devoted to boundary conditions that are crucial for the feasibility of the bidimensional EMD. The study of the behavior of the decomposition on a different kind of image shows its efficiency in terms of computational cost, and the decomposition of Gaussian white noises leads to bidimensional selective filter banks.

We first recall the relation between discrete B-splines and the control points of B-splines. We then use some convergence properties of the control points of B-splines to derive a new algorithm that approximates the wavelet decomposition at rational scales and rational location. We conclude the paper by some numerical experiments illustrating the behavior of our algorithm and by a discussion on an efficient implementation of the proposed method.