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Scattering methods are widely used in many research areas to analyze and resolve material structures. Given the importance, a large number of full textbooks are devoted to this topic. However, technical details in experiments and…
Convolutive Non-Negative Matrix Factorization model factorizes a given audio spectrogram using frequency templates with a temporal dimension. In this paper, we present a convolutional auto-encoder model that acts as a neural network…
Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two…
Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics are taking place on a discrete half-space. All operators are represented graphically. The expressions…
There is still a gap in understanding phonons scattering by geometrical defects at the nanoscale, and it remains a significant challenge for heat transfer management in nanoscale devices and systems. In this study, we aim to explore the…
Space-time materials are obtained by modulating a physical medium with a traveling-wave perturbation of one or several of its constitutive parameters, such as the density or the bulk modulus in the case of acoustic materials. When this…
We introduce a ScatterNet that uses a parametric log transformation with Dual-Tree complex wavelets to extract translation invariant representations from a multi-resolution image. The parametric transformation aids the OLS pruning algorithm…
This article explains how to apply time--frequency scattering, a convolutional operator extracting modulations in the time--frequency domain at different rates and scales, to the re-synthesis and manipulation of audio textures. After…
In a recent letter [Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering…
We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…
We propose a novel approach for time-scale modification of audio signals. Unlike traditional methods that rely on the framing technique or the short-time Fourier transform to preserve the frequency during temporal stretching, our neural…
This paper is concerned with acoustic scattering from a sound-soft trapezoidal surface in two dimensions. The trapezoidal surface is supposed to consist of two horizontal half-lines pointing oppositely, and a single finite vertical line…
Waves, such as light and sound, inherently bounce and mix due to multiple scattering induced by the complex material objects that surround us. This scattering process severely scrambles the information carried by waves, challenging…
A wave propagating through a scattering medium typically yields a complex temporal field distribution. Over the years, a number of procedures have emerged to shape the temporal profile of the field in order to temporally focus its energy on…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
In this work, we present a method for learning interpretable music signal representations directly from waveform signals. Our method can be trained using unsupervised objectives and relies on the denoising auto-encoder model that uses a…
A spatially varying blur kernel $h(\mathbf{x},\mathbf{u})$ is specified by an input coordinate $\mathbf{u} \in \mathbb{R}^2$ and an output coordinate $\mathbf{x} \in \mathbb{R}^2$. For computational efficiency, we sometimes write…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
We demonstrate the successful use of scattering representations without further compression for simulation-based inference (SBI) with images (i.e. field-level), illustrated with a cosmological case study. Scattering representations provide…
Tone Transfer is a novel deep-learning technique for interfacing a sound source with a synthesizer, transforming the timbre of audio excerpts while keeping their musical form content. Due to its good audio quality results and continuous…