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We analyze the asymptotic performance of sparse signal recovery from noisy measurements. In particular, we generalize some of the existing results for the Gaussian case to subgaussian and other ensembles. An achievable result is presented…

Information Theory · Computer Science 2009-04-30 Paul Tune , Sibiraj Bhaskaran Pillai , Stephen Hanly

Standardized laboratory characterizations for absorbing materials rely on idealized sound field assumptions, which deviate largely from real-life conditions. Consequently, \emph{in-situ} acoustic characterization has become essential for…

Sound · Computer Science 2026-02-13 Yuanxin Xia , Xinyan Li , Matteo Calafà , Allan P. Engsig-Karup , Cheol-Ho Jeong

The reconstruction of the unknown acoustic source is studied using the noisy multiple frequency data on a remote closed surface. Assume that the unknown source is coded in a spatial dependent piecewise constant function, whose support set…

Numerical Analysis · Mathematics 2019-07-23 Zhiliang Deng , Xiaomei Yang , Jiangfeng Huang

This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity regularization does not necessarily produce adequate results…

Numerical Analysis · Mathematics 2023-05-25 Ole Løseth Elvetun , Bjørn Fredrik Nielsen

Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…

Analysis of PDEs · Mathematics 2016-07-20 Roland Griesmaier , John Sylvester

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…

Optimization and Control · Mathematics 2020-02-05 Albert Akhriev , Jakub Marecek , Andrea Simonetto

In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…

Information Theory · Computer Science 2015-11-02 Souleymen Sahnoun , El-Hadi Djermoune , David Brie , Pierre Comon

We explore the possibility for using boundary measurements to recover a sparse source term f(x) in the potential equation. Employing weighted sparsity regularization and standard results for subgradients, we derive simple-to-check criteria…

Optimization and Control · Mathematics 2023-11-06 Ole Løseth Elvetun , Bjørn Fredrik Nielsen

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

The hearing sense on a mobile robot is important because it is omnidirectional and it does not require direct line-of-sight with the sound source. Such capabilities can nicely complement vision to help localize a person or an interesting…

Robotics · Computer Science 2016-02-29 Jean-Marc Valin , François Michaud , Jean Rouat , Dominic Létourneau

Acoustic signal processing in the spherical harmonics domain (SHD) is an active research area that exploits the signals acquired by higher order microphone arrays. A very important task is that concerning the localization of active sound…

Audio and Speech Processing · Electrical Eng. & Systems 2024-01-29 Maximo Cobos , Mirco Pezzoli , Fabio Antonacci , Augusto Sarti

Relative impulse responses between microphones are usually long and dense due to the reverberant acoustic environment. Estimating them from short and noisy recordings poses a long-standing challenge of audio signal processing. In this paper…

Sound · Computer Science 2016-11-17 Zbynek Koldovsky , Jiri Malek , Sharon Gannot

The study and application of signal detection techniques based on cross-correlation method for acoustic transient signals in noisy and reverberant environments are presented. These techniques are shown to provide high signal to noise ratio,…

Instrumentation and Detectors · Physics 2015-02-19 S. Adrián-Martínez , M. Ardid , M. Bou-Cabo , I. Felis , C. Llorens , J. A. Martínez-Mora , M. Saldaña

Room acoustics is mainly based on the reverberation theories of Saine and Eyring. In Sabine's theory however, the reverberation time does not reach zero, even if the condition of absolute absorption is fulfilled. Eyring revised…

Classical Physics · Physics 2024-10-01 Toshiki Hanyu

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…

Machine Learning · Computer Science 2025-08-14 Tristan S. W. Stevens , Hans van Gorp , Faik C. Meral , Junseob Shin , Jason Yu , Jean-Luc Robert , Ruud J. G. van Sloun

In this work we study the statistical model of source localization based on Range Difference measurements. We investigate the case of planar localization of a source using a minimal configuration of three non aligned receivers. Our analysis…

Information Theory · Computer Science 2016-06-28 Marco Compagnoni , Roberto Notari , Fabio Antonacci , Augusto Sarti

We present an indoor acoustic simulation framework that supports both ultrasonic and audible signaling. The framework opens the opportunity for fast indoor acoustic data generation and positioning development. The improved…

Audio and Speech Processing · Electrical Eng. & Systems 2023-06-22 Daan Delabie , Chesney Buyle , Bert Cox , Liesbet Van der Perre , Lieven De Strycker

This work is dedicated to novel uniqueness results and high resolution sampling methods for source support from multi-frequency sparse far field patterns. With a single pair of observation directions $\pm\hat{x}$, we prove that the lines…

Numerical Analysis · Mathematics 2025-05-23 Xiaodong Liu , Qingxiang Shi

Separating audio mixtures into individual instrument tracks has been a long standing challenging task. We introduce a novel weakly supervised audio source separation approach based on deep adversarial learning. Specifically, our loss…

Sound · Computer Science 2018-05-18 Ning Zhang , Junchi Yan , Yuchen Zhou

This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…

Numerical Analysis · Mathematics 2017-02-09 Frederic Weidling , Thorsten Hohage
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