相关论文: Une ou deux composantes ? La r\'eponse de la diffu…
With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by…
The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode…
The spatial structure of the inhomogeneity in a disordered medium determines how waves scatter and propagate in it. We present a theoretical model of how the Fourier components of the disorder control wave scattering in a two-dimensional…
This paper introduces a Deep Scattering network that utilizes Dual-Tree complex wavelets to extract translation invariant representations from an input signal. The computationally efficient Dual-Tree wavelets decompose the input signal into…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the…
This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an…
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time…
In this work, we develop machine learning techniques to study nonperturbative scattering amplitudes. We focus on the two-to-two scattering amplitude of identical scalar particles, setting the double discontinuity to zero as a simplifying…
Several differentiating algorithms of the noisy signals are considered. The proposed wavelet based technique is compared with others based on the Fourier transform and the finite differences. The accuracy of the calculations for different…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
The need of mathematically formulate relations between composite materials' properties and its resonance response is growing. This is due the fast technological advancement in micro-material manufacturing, present in chips for instance. In…
Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in…
This work presents a multiple scattering formulation of two dimensional acoustic metamaterials. It is shown that in the low frequency limit multiple scattering allows us to define frequency-dependent effective acoustic parameters for arrays…
We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting plane wave. The first scheme is for locating scatterers of…