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The two-dimensional grid-free compressed sensing method with planar microphone arrays is expected to achieve super-resolution direction-of-arrival (DOA) estimation for acoustic sources in the hemispherical space in front of array. The existing methods are not yet well compatible with arbitrary planar array geometries. In this paper, we aim to break this limitation and explore a novel method applicable to arbitrary planar array geometries. First, the covariance between source-induced signals at arbitrary two microphones is formulated as related to the two-dimensional inverse Fourier transform of the source strength. Then, a mathematical model with a source sparsity constraint is built in the continuous domain to denoise the covariances of measured signals, which can be solved by decoupled positive semidefinite programming. Finally, the DOAs are extracted from the solution of the mathematical model via a matrix pencil and pairing method. Simulation and experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Methods from the field of computer graphics are the foundation for the representation of geological structures in the form of geological models. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered, and the capacities and limitations of different algorithms are not always evident. In this work, we therefore review surface-based geological modelling methods from both a geological and computer graphics perspective. Specifically, we investigate the use of NURBS (non-uniform rational B-splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of the two approaches. Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention—even if subdivision surfaces support arbitrary topologies and watertight boundary representation, two aspects that make them an appealing choice for complex geological modelling. It is worth mentioning that watertight models are an important basis for subsequent process simulations. Many complex geological structures require a combination of smooth and sharp edges. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterise the resistance of a mesh structure to the subdivision procedure. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology, is described. Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison with the complex geological structure. [ABSTRACT FROM AUTHOR]

Compressive beamforming with a planar microphone array can effectively estimate the two-dimensional directions-of-arrival and quantify the strengths of acoustic sources. Due to the superiorities of overcoming the basis mismatch issue of the conventional grid-based method and improving the performance of the single-snapshot grid-free method, the multiple-snapshot grid-free method has become the current research focus. Its existing atomic norm minimization (ANM) based strategy blocks high resolution because it cannot work well for sources with a small separation. This paper commits itself to remedying this drawback. After revealing the cause for this drawback, we present an iterative reweighted ANM (IRANM) approach. Both simulations and experiments demonstrate that compared with the ANM-based two-dimensional multiple-snapshot grid-free compressive beamforming, the IRANM-based one enjoys not only the enhanced resolution but also the stronger denoising ability and the higher identification accuracy. [ABSTRACT FROM AUTHOR]

• A grid-free compressive beamforming method is proposed based on prolate spheroidal wave functions. • It is compatible with arbitrary linear microphone arrays. • It can identify sources accurately, even using only a single snapshot. • The increase in snapshots helps the method perform better. Grid-free compressive beamforming is a new attractive method for acoustic source identification based on compressive sensing theory, which extracts the source information from the microphone array measurements without discretizing the target source region. In the framework of linear microphone array measurements, many studies have been carried out around this method. They have strict requirements on the distribution of microphones. Specifically, only the uniform arrays with equally spaced microphones and sparse arrays consisting of a selection of microphones from uniform arrays are available. In this paper, based on the prolate spheroidal wave functions, we propose a grid-free compressive beamforming method compatible with arbitrary linear microphone arrays. Some examples are conducted to demonstrate the correctness and superiority of the proposed method. Plenty of Monte Carlo simulations are performed to reveal the effects of source coherence, source separation, noise, and number of snapshots. This study helps to promote the popularization and application of grid-free compressive beamforming method and offers the possibility to improve the acoustic source identification performance by optimizing microphone distribution. [ABSTRACT FROM AUTHOR]

In this work, a new grid-free global optimization algorithm that combined the image source model(ISM) and state transition algorithm(STA) was proposed to realize the sound source localization in reverberant environments. The simulation results show that only first-order mirror sources being kept can ensure localization accuracy. Compared with de-reverberation beamforming, the localization results of the proposed algorithm have no sidelobes and smaller mainlobes. Compared with the differential evolution(DE) algorithm, STA can converge to smaller fitness values, which can achieve more accurate sound source localization in reverberant environments. Meanwhile, the proposed algorithm can be applied to both single-source and multi-source localization in practical scenarios. The experimental results show that the proposed algorithm can locate the sound source accurately in reverberant environments. • A 3D grid-free de-reverberation sound sources localization algorithm is proposed. • It shows no sidelobes and smaller mainlobes than the de-reverberation beamforming. • It achieves more accurate results than the differential evolution algorithm. [ABSTRACT FROM AUTHOR]

• Two-dimensional grid-free compressive beamforming for spherical arrays is proposed. • It can avoid basis mismatch defect and enjoys significant accuracy superiority. • It can identify sources accurately and panoramically, even only with one snapshot. • The increase in snapshots helps the method perform better. Compressive beamforming based on microphone array measurements and compressive sensing theory is an emerging and practical acoustic source identification technology. The grid-free compressive beamforming that treats the target source region as a continuum has attracted tremendous attention due to the advantage of circumventing the basis mismatch defect caused by the gridding. The grid-free methods have been developed for the linear and the planar microphone array measurements to identify sources in a local region. In contrast, for the spherical microphone array measurements suitable for 360° panoramic identification, the current research mainly focuses on grid-based methods. In this paper, we propose a two-dimensional grid-free compressive beamforming method with spherical microphone arrays. First of all, the relationship between the spherical harmonic function vector and the two-dimensional Fourier basis function vector is determined. Then, the mathematical model relating the measured sound pressures to the source distribution is built under a continuous setting. Next, a source sparsity constraint is imposed based on the total variation norm to solve the mathematical model, and its dual problem is deduced. Subsequently, the dual problem is solved by positive semidefinite programming. Finally, the DOAs of sources are estimated through polynomial rooting and utilizing the dual optimal variables, and the source strengths are quantified via least-square fitting. An experimental case is conducted to examine the practicability and superiority of the proposed method to the existing grid-based compressive beamforming method. Plenty of Monte Carlo simulations are carried out to disclose the influence of the source coherence, the angular distance between sources, the noise, the number of snapshots and the number of microphones. This study offers a new approach for the accurate and 360° panoramic identification of acoustic sources. [ABSTRACT FROM AUTHOR]