相关论文: On sound ranging in Hilbert space

Beamforming is a signal processing technique. It has been studied in many areas such as radar, sonar, seismology and wireless communications, to name but a few. It can be used for a myriad of purposes, such as detecting the presence of a…

The following development of the well-known "vertical modes and horizontal rays" approach for acoustic waves propagation in shallow water, introduced in different works, is studied. In this approach we study so-called space-time horizontal…

We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…

Sound source localisation is used in many consumer devices, to isolate audio from individual speakers and reject noise. Localization is frequently accomplished by ``beamforming'', which combines phase-shifted audio streams to increase power…

Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…

We consider reachability decision problems for linear dynamical systems: Given a linear map on $\mathbb{R}^d$ , together with source and target sets, determine whether there is a point in the source set whose orbit, obtained by repeatedly…

We present a unified model capable of simultaneously grounding both spoken language and non-speech sounds within a visual scene, addressing key limitations in current audio-visual grounding models. Existing approaches are typically limited…

We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…

Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…

In this paper, the problem of target localization in the presence of outlying sensors is tackled. This problem is important in practice because in many real-world applications the sensors might report irrelevant data unintentionally or…

Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…

Separating an audio scene into isolated sources is a fundamental problem in computer audition, analogous to image segmentation in visual scene analysis. Source separation systems based on deep learning are currently the most successful…

If the speed of sound were vastly larger in the early Universe a near scale-invariant spectrum of density fluctuations could have been produced even if the Universe did not submit to conventional solutions to the horizon problem. We examine…

Multichannel measurement with hundreds of channels essentially covers all measurable degrees of freedom of a curl and source free vector field, like the magnetic field in a volume free of current sources (e.g. in magnetoencephalography,…

Motivated by the simulation of stable random fields, we consider the issue of discrete approximations of independently scattered stable noise. Two approaches are proposed: grid approximations available when the underlying space is $\bbR^d$…

In this paper we solve the polarization problem for real Hilbert spaces, a long-standing conjecture that had remained open for nearly three decades. We also confirm that the only extremal configurations are orthonormal sets. These are…

We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a…

Source localization is widely used in many areas including GPS, but the influence of possible noises is not so negligible. Many optimization methods are attempted to alleviate different kinds of noises. Needless to say the stability of the…

In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…