Related papers: Analysis of time-frequency scattering transforms
This paper introduces Gabor scattering, a feature extractor based on Gabor frames and Mallat's scattering transform. By using a simple signal model for audio signals specific properties of Gabor scattering are studied. It is shown that for…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
In this paper we construct directionally sensitive functions that can be viewed as directional time-frequency representations. We call such a sequence a rotational uniform covering frame and by studying rotations of the frame, we derive the…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier…
We analyze energy decay for deep convolutional neural networks employed as feature extractors, including Mallat's wavelet scattering transform. For time-frequency scattering transforms based on Gabor filters, previous work has established…
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends…
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time…
We study wave propagation through a one-dimensional array of subwavelength resonators with periodically time-modulated material parameters. Focusing on a high-contrast regime, we use a scattering framework based on Fourier expansions and…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
We study an aspect of the following general question: which properties of a signal can be characterized by its scattering transform? We show that the energy contained in high order scattering coefficients is upper bounded by the energy…
A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…
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…
The presence of a scattering medium in the imaging path between an object and an observer is known to severely limit the visual acuity of the imaging system. We present an approach to circumvent the deleterious effects of scattering, by…
We present an efficient and precise framework to quantum simulate the dynamics of the ultra-relativistic quark-nucleus scattering. This framework employs the eigenbasis of the asymptotic scattering system and implements a compact scheme for…
A forward model is presented to an inverse scattering problem that arises in the application of reflective Fourier ptychographic microscopy. The model allows us to determine the 3D distributions of refractive index for weakly scattering…
The transfer matrix of scattering theory in one dimension can be expressed in terms of the time-evolution operator for an effective non-unitary quantum system. In particular, it admits a Dyson series expansion which turns out to facilitate…
We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…