Acoustic Inverse Problem Research Articles

Enhancing Ischemic Stroke Evaluation by a Model-Based Photoacoustic Tomography Algorithm.

Ischemic stroke (IS) is characterized by the sudden interruption of blood supply to the brain, resulting in neurological impairments and even mortality. Photoacoustic computed tomography (PACT) integrates the high contrast of optical imaging and the penetration of ultrasound imaging, enabling non-invasive IS evaluation. However, the image reconstruction quality significantly affects the oxyhemoglobin saturation (sO2) estimation. This study investigates a model-based with total variation minimized by augmented Lagrangian and alternating direction (MB-TVAL3) approach and compared it with the widely used back-projection (BP) and delay-and-sum (DAS) algorithms. Both simulations and invivo experiments are conducted to validate the performance of the MB-TVAL3 algorithm, showing a higher sO2 estimation accuracy and sensitivity in detecting infarct area compared to BP and DAS. The findings of this study emphasize the impact of acoustic inverse problem on the accuracy of sO2 estimation and the proposed approach offers valuable support for IS evaluation and cerebrovascular diagnosis.

A Novel Time-Domain Direct Sampling Approach for Inverse Scattering Problems in Acoustics

A Novel Time-Domain Direct Sampling Approach for Inverse Scattering Problems in Acoustics

A simple method improving acoustic mode identification capability based on genetic algorithms

This letter develops a simple approach of duct mode identification and reconstruction based on genetic algorithms, which can extend the azimuthal mode order range compared to the conventional method based on the (spatial) discrete Fourier transform. The underlying principle is reconstructing the dominant mode from the modal identification forward model through optimization by exploiting the sparsity of the mode amplitude vector. The performance is experimentally demonstrated for detections of one and two azimuthal modes under noisy conditions with nondominant modes. Overall, the proposed genetic-algorithm-based framework for solving acoustic inverse problems is beneficial to duct acoustic testing, particularly design evaluations of fan blades and acoustic liners for aeroengines.

Preface: Special Issue on Inverse Problems in Acoustics

Preface: Special Issue on Inverse Problems in Acoustics

A novel sampling method for time domain acoustic inverse source problems

The time domain acoustic inverse source problems of the wave equation have been widely used in many fields, such as radar detection and underwater sonar. This paper is concerned with the inverse acoustic scattering problems of reconstructing time-dependent multiple point sources and sources on a curve L of the form λ(t)τ(x)δ L (x). A direct sampling method with a novel indicator function is proposed to reconstruct the sources. The sampling method is easy to implement and low in calculation cost. Based on the sampling method, numerical algorithms are provided to get the positions and intensities of the sources. Through theoretical analysis of the indicator function and numerical experiments, the effectiveness of the proposed method is verified.

Modeling the Solution of the Acoustic Inverse Problem of Scattering for a Three-Dimensional Nonstationary Medium

Modeling the Solution of the Acoustic Inverse Problem of Scattering for a Three-Dimensional Nonstationary Medium

Error estimation to the direct sampling method for the inverse acoustic source problem with multi-frequency data

Error estimation to the direct sampling method for the inverse acoustic source problem with multi-frequency data

Quantitative photoacoustic tomography: modeling and inverse problems.

Quantitative photoacoustic tomography (QPAT) exploits the photoacoustic effect with the aim of estimating images of clinically relevant quantities related to the tissue's optical absorption. The technique has two aspects: an acoustic part, where the initial acoustic pressure distribution is estimated from measured photoacoustic time-series, and an optical part, where the distributions of the optical parameters are estimated from the initial pressure. Our study is focused on the optical part. In particular, computational modeling of light propagation (forward problem) and numerical solution methodologies of the image reconstruction (inverse problem) are discussed. The commonly used mathematical models of how light and sound propagate in biological tissue are reviewed. A short overview of how the acoustic inverse problem is usually treated is given. The optical inverse problem and methods for its solution are reviewed. In addition, some limitations of real-life measurements and their effect on the inverse problems are discussed. An overview of QPAT with a focus on the optical part was given. Computational modeling and inverse problems of QPAT were addressed, and some key challenges were discussed. Furthermore, the developments for tackling these problems were reviewed. Although modeling of light transport is well-understood and there is a well-developed framework of inverse mathematics for approaching the inverse problem of QPAT, there are still challenges in taking these methodologies to practice. Modeling and inverse problems of QPAT together were discussed. The scope was limited to the optical part, and the acoustic aspects were discussed only to the extent that they relate to the optical aspect.

Localization of cyclostationary acoustic sources via cyclostationary beamforming and its high spatial resolution implementation

The localization of cyclostationary sound sources is important for rotating machinery noise source identification and fault diagnosis. Cyclostationary sound sources are a special class of nonstationary sound sources, which exhibit periodic changes in statistics. Most of the conventional sound source identification methods are based on the stationary sound source assumption, which do not consider the cyclostationarity of the radiated sound field by rotating machinery. Thus, they are hard to localize the acoustic sources with different cyclic frequencies. In this paper, a novel technique of localizing the cyclostationary acoustic sources with different cyclic frequencies is proposed. First, the cyclostationary conventional beamforming (CSCBF) method is deviated. In CSCBF, the cyclic-cross-spectral matrix (CCSM) is defined considering all the cross cyclic spectral correlation (CSC) between different microphones in the array. The left steering vector and right steering vector are constructed to focus the CCSM on each scanning grid point at a given combination of cyclic frequency and spectral frequency. Then, the high resolution cyclostationary beamforming (HR-CSBF) is further developed to improve the spatial resolution of CSCBF. In HR-CSBF, two linear equations according to the property of CSC is established as the acoustic inverse problems. With the sparse distribution of the cyclostationary sources in the space as the prior knowledge, the iterated Bayesian focusing (IBF) is utilized to obtain a robust and sparse solution in HR-CSBF. Numerical simulations and experiments are conducted to validate the proposed methods. To explore the potential applications of the proposed methods, the localization of high pressure pump (HPP) and rolling bearing with outer-race failure are also used to evaluate the effectiveness of the proposed methods. It turns out that both CSCBF and HR-CSBF can localize the cyclostationary sources with different cyclic frequencies. Compared with CSCBF, HR-CSBF can achieve a higher spatial resolution in the obtained acoustic map.

A neural network warm-start approach for the inverse acoustic obstacle scattering problem

In this paper, we consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the object. One of the standard approaches for solving this problem is to reformulate it as an optimization problem: finding the boundary of the domain that minimizes the L2 distance between computed values of the scattered field and the given measurement data. The optimization problem is computationally challenging since the local set of convexity shrinks with increasing frequency and results in an increasing number of local minima in the vicinity of the true solution. In many practical experimental settings, low frequency measurements are unavailable due to limitations of the experimental setup or the sensors used for measurement. Thus, obtaining a good initial guess for the optimization problem plays a vital role in this environment.We present a neural network warm-start approach for solving the inverse scattering problem, where an initial guess for the optimization problem is obtained using a trained neural network. We demonstrate the effectiveness of our method with several numerical examples. For high frequency problems, this approach outperforms traditional iterative methods such as Gauss-Newton initialized without any prior (i.e., initialized using a unit circle), or initialized using the solution of a direct method such as the linear sampling method. The algorithm remains robust to noise in the scattered field measurements and also converges to the true solution for limited aperture data. However, the number of training samples required to train the neural network scales exponentially in frequency and the complexity of the obstacles considered. We conclude with a discussion of this phenomenon and potential directions for future research.

On the application of MUSIC algorithm for identifying short sound-hard arcs in limited-view inverse acoustic problem

For proper application of the MUltiple SIgnal Classification (MUSIC) algorithm for imaging short, linear sound-hard arcs, one needs a priori information of the unit outward normal vector on each arc. Due to this reason, a set of directions was applied to estimate, which caused the imaging procedure’s slowness. Applying a unit vector instead of the estimation is natural to avoid this difficulty. However, no relevant mathematical theory has been developed to explain the various phenomena in simulation results. Here, we consider applying MUSIC without a priori information of the arcs. To this end, we introduce the imaging functions of MUSIC with and without information on the unit outward vector on the arcs. We analyze their mathematical structure by establishing an infinite series of Bessel functions and the range of incident/observation directions and discuss their properties. This is based on the physical factorization of the multi-static response (MSR) matrix that separates the incoming plane-wave information from the unknown density information. Numerical simulation results with noisy data are conducted for small and extended arcs to support the theoretical result.

A Bayesian Framework of Non-Synchronous Measurements at Coprime Positions for Sound Source Localization With High Resolution

The noise distribution in the mechanical system is tightly connected to the structure design and particular operating conditions. The noise source localization can effectively assist with the operating condition monitoring and noise reduction design of the mechanical device. The performance limitation of the array aperture for lower frequency acoustic localization is broken up by the non-synchronous measurement at coprime positions (CP-NSM), while this method has high uncertainty and requires an efficient adaptive regularization method to solve its corresponding acoustic inverse problem. The algorithms under the Bayesian framework with Student-t priors (variational Bayesian approximation and subspace variational Bayesian) are derived and deployed to solve the acoustic inverse problem in the CP-NSM method, and the results are compared with those obtained by the interior-point method and the alternating direction method of the multipliers algorithm. The proposed Bayesian methods have the advantages of adaptive regularization parameter estimation, which can reduce the influence of various interferences in CP-NSM. At the same time, in addition to using simulations and experiments in the anechoic chambers, the proposed Bayesian algorithms are validated further in real industrial applications. The proposed method is applied to improve the noise reduction design of the centrifugal fan, a mechanical device containing more information from noise sources.

Muti-frequency extended sampling method for the inverse acoustic source problem

<abstract><p>We consider the reconstruction of the compact support of an acoustic source given multiple frequency far field data. We propose a multi-frequency extended sampling method (MESM). The MESM computes the solutions of some ill-posed integral equations and constructs an indicator function to image the source. The behavior of the indicator function is justified. The method is fast and easy to implement. Various numerical examples are presented to show the effectiveness of the MESM for both frequency-independent and frequency-dependent sources.</p></abstract>

Deterministic-statistical approach for an inverse acoustic source problem using multiple frequency limited aperture data

We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the source. The Dirichlet eigenfunctions of the disc are used to expand the source function. Then the inverse problem is recast as a statistical inference problem and the Bayesian inversion is employed to reconstruct the coefficients of the eigen-expansion for the source function. The stability of the statistical inverse problem with respect to the measured data is justified in the sense of Hellinger distance. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings (MH) algorithm is implemented to explore the posterior density function. Numerical examples show that the proposed method is effective for both smooth and non-smooth sources.

Linearized boundary control method for an acoustic inverse boundary value problem

We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of Hölder-type stability in two and higher dimensions. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility.

The acoustic inverse problem in the inhomogeneous medium by iterative Bayesian focusing algorithm

A random inhomogeneous sound propagation medium is considered in acoustic imaging, which is modeled by a random function of the spatial medium. The inhomogeneity of the sound propagation environment can cause large errors in the modeling and measurement of acoustic imaging. Since the wave equation contains random variables, Green’s function no longer has a specific analytical solution. The main work of this paper is as follows: (1) The acoustic inverse problem is considered in the inhomogeneous sound field, which is expressed according to predefined statistical information; (2) Karhunen-Loève expansion is used to simplify the proposed inhomogeneous propagation sound field, and the numerical solution of Green’s function is used instead of the original analytical solution; (3) A dual-driven (including data-driven and knowledge-driven) algorithm based on the Bayesian framework is developed to achieve acoustic imaging, which is implemented through the joint estimation of the aperture function and the sparse prior. Finally, the proposed model and algorithm are verified by a numerical simulation. The proposed algorithm is compared with conventional beamforming in terms of localization accuracy and sound power quantization. The simulation results show that the inhomogeneous sound field can be represented by a small number of random variables, and the proposed dual-drive algorithm can accurately achieve acoustic imaging in the inhomogeneous propagation environment.

A Conditioned Probabilistic Method for the Solution of the Inverse Acoustic Scattering Problem

In the present work, a novel stochastic method has been developed and investigated in order to face the time-reduced inverse scattering problem, governed by the Helmholtz equation, outside connected or disconnected obstacles supporting boundary conditions of Dirichlet type. On the basis of the stochastic analysis, a series of efficient and alternative stochastic representations of the scattering field have been constructed. These novel representations constitute conceptually the probabilistic analogue of the well known deterministic integral representations involving the famous Green’s functions, and so merit special importance. Their advantage lies in their intrinsic probabilistic nature, allowing to solve the direct and inverse scattering problem in the realm of local methods, which are strongly preferable in comparison with the traditional global ones. The aforementioned locality reflects the ability to handle the scattering field only in small bounded portions of the scattering medium by monitoring suitable stochastic processes, confined in narrow sub-regions where data are available. Especially in the realm of the inverse scattering problem, two different schemes are proposed facing reconstruction from the far field and near field data, respectively. The crucial characteristic of the inversion is that the reconstruction is fulfilled through stochastic experiments, taking place in the interior of conical regions whose base belong to the data region, while their vertices detect appropriately the supporting surfaces of the sought scatterers.

Localized MFS for three‐dimensional acoustic inverse problems on complicated domains

AbstractThis paper proposes a semi‐analytical and local meshless collocation method, the localized method of fundamental solutions (LMFS), to address three‐dimensional (3D) acoustic inverse problems in complex domains. The proposed approach is a recently developed numerical scheme with the potential of being mathematically simple, numerically accurate, and requiring less computational time and storage. In LMFS, an overdetermined sparse linear system is constructed by using the known data at the nodes on the accessible boundary and by making the remaining nodes satisfy the governing equation. In the numerical procedure, the pseudoinverse of a matrix is solved via the truncated singular value decomposition, and thus the regularization techniques are not needed in solving the resulting linear system with a well‐conditioned matrix. Numerical experiments, involving complicated geometry and the high noise level, confirm the effectiveness and performance of the LMFS for solving 3D acoustic inverse problems.

Acoustic tomography of temperature and velocity fields by using the radial basis function and alternating direction method of multipliers

Considering the acoustic refraction effect, an investigation of simultaneously visualizing the temperature and velocity fields is carried out by using the combined meshfree radial basis function and alternating direction method of multipliers (RBF-ADMM). The radial basis function is introduced to recover the null-space component. It assumes that the reconstructed fields are continuous functions according to their nature, which, therefore, adds the prior information of the continuity in the fields’ reconstruction. Meanwhile, the alternating direction method of multipliers with improving anti-noise capacity is employed to iteratively resolve the inverse acoustic tomographic problem in low Mach number, which makes the parallel implementation and distributed optimization possible. Different from the traditional methods for solving boundary value problems, a fast two-point ray-tracing algorithm is introduced to trace the curved sound waves more efficiently. Proof-of-concept demonstrations including the representative temperature and aerodynamic fields are performed. For the two scenarios of two-peak and two-vortex inhomogeneous fields with 10% measurement errors, the averaged absolute errors of the reconstructed temperature fields are 120.7 K, and 39.9 K, respectively, and that of the reconstructed velocity fields are 0.24 m/s and 1.23 m/s, respectively. In addition, a data-based verification, which depicts the Karman vortex street phenomenon, is carried out to prove the ability of this method. All the results confirm the feasibility and effectiveness of the proposed RBF-ADMM in simultaneously reconstructing the temperature and velocity fields under different complicated environment. The proposed method for visualizing the arbitrary temperature and velocity fields will provide crucial input for control system such as the engines and boilers to optimize the thermal fluid and combustion process.

Sparsity-enhanced equivalent source method for acoustic source reconstruction via the Generalized Minimax-Concave penalty

The Equivalent Source Method (ESM) is a powerful technique for acoustic source reconstruction, which has been widely used in noise control and machinery fault detection. Because the inverse acoustic source reconstruction problem is typically ill-conditioned, regularization techniques are often adopted in ESM to achieve meaningful solutions. Based on the sparse distribution assumption of acoustic sources, sparse regularization can be utilized in ESM to promote the spatial resolution of reconstructed results. Existing sparse ESMs often adopt convex l1 norm or nonconvex lp norm as the regularization terms. However, l1 norm-regularized ESM suffers from an insufficient sparsity-inducing problem, which decreases the spatial resolution and reconstruction accuracy. Meanwhile, reconstructed results of lp norm-regularized ESM are often unstable due to multiple local minimas. In this paper, a sparsity-enhanced ESM is proposed, which introduces a nonconvex Generalized Minimax-Concave (GMC) penalty into ESM as the regularization term. The GMC penalty can enhance the sparsity of solutions and simultaneously maintain the convexity of the overall objective function in acoustic source reconstruction. Consequently, the GMC penalty-regularized ESM can improve the spatial resolution and reconstruction accuracy of the reconstructed results. To solve the acoustic source reconstruction problem rapidly, a computation framework based on Alternating Direction Method of Multipliers (ADMM) is derived. Simulation studies indicate that the proposed method can improve the acoustic source reconstruction accuracy in a wide frequency band, compared with existing l1 and lp norm-regularized ESMs. Two experimental cases further verify that the proposed sparsity-enhanced ESM can effectively reconstruct the acoustic sources with high spatial resolution and reconstruction accuracy at higher frequencies.