Sparsity-based sound field reconstruction Koyama, Shoichi
Acoustical Science and Technology,
2020/01/01, 2020-1-1, 20200101, Letnik:
41, Številka:
1
Journal Article
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Estimating and interpolating a sound field from measurements using multiple microphones are fundamental tasks in sound field analysis for sound field reconstruction. The sound field reconstruction ...inside a source-free region is achieved by decomposing the sound field into plane-wave or harmonic functions. When the target region includes sources, it is necessary to impose some assumptions on the sources. Recently, it has been increasingly popular to apply sparse representation algorithms to various sound field analysis methods. In this paper, we present an overview of sparsity-based sound field reconstruction methods and also demonstrate their application to sound field recording and reproduction.
This paper investigates sound-field modeling in a realistic reverberant setting. Starting from a few point-like microphone measurements, the goal is to estimate the direct source field within a whole ...three-dimensional (3-D) space around these microphones. Previous sparse sound field decompositions assumed only a spatial sparsity of the source distribution, but could generally not handle reverberation. We here add an explicit model of the reverberant sound field, that has two components: the first component sparse in the plane-wave domain, the other component low-rank as a multiplication of transfer functions and source signals. We derive the corresponding decomposition algorithm based on the alternating direction method of multipliers. We furthermore provide empirical rules for tuning the two parameters to be set in the algorithm. Numerical and experimental results indicate that the decomposition and reconstruction performances are significantly improved, in the case of reverberant environments.
A sound field recording method based on spherical or circular harmonic analysis for arbitrary array geometry and directivity of microphones is proposed. In current methods based on harmonic analysis, ...a sound field is decomposed into harmonic functions with a center given in advance, which is called a global origin, and their coefficients are obtained up to a certain truncation order using microphone measurements. However, the accuracy of the reconstructed sound field depends on the predefined position of the global origin and the truncation order, which makes it difficult to apply this technique to an asymmetric array since the criterion to determine the position of the global origin and the truncation order is not obvious. We formulate an estimate of the harmonic coefficients on the basis of infinite-order analysis. This formulation enables us to estimate the harmonic coefficients at an arbitrary desired position independently of the position of the global origin without truncation errors. Numerical simulation results indicated that the proposed method makes it possible to avoid performance degradation caused by inappropriate setting of the global origin.
A wave field estimation method exploiting prior information on source direction is proposed. First, we formulate a wave field estimation problem as regularized least squares, where the norm of the ...wave field is used for a regularization term. The norm of the wave field is defined on the basis of the weighting function that reflects the prior information on the source direction. We derive the closed-form solution using theories on Hilbert spaces. Results of numerical experiments indicated that high estimation accuracy can be achieved by using the proposed method in comparison with other current methods that do not use any prior information.
•This is the first work to decompose and reconstruct a sound field based on the reciprocity gap functional (RGF) in the spherical harmonic domain.•As opposed to the sparse-representation algorithms, ...the proposed method does not require the discretization of the target region into grid points.•The proposed method makes it possible to avoid decomposition errors of off-grid sources and high computational cost of sparse representation.•The RGF is applied to the sound field decomposition, which enables to decompose the sound field as a closed-form solution with the flexible arrangement of microphones.
A sound field decomposition method based on the reciprocity gap functional (RGF) in the spherical harmonic domain is proposed. To estimate and reconstruct a continuous sound field including sources by using multiple microphones, an intuitive and powerful strategy is to decompose the sound field into Green’s functions. Sparse-representation algorithms have been applied to this decomposition problem; however, it requires the discretization of the target region into grid points to construct a dictionary matrix. Discretization-based methods lead to decomposition errors of off-grid sources and high computational cost of sparse representation. We apply the RGF to sparse sound field decomposition, which makes it possible to decompose the sound field as a closed-form solution without discretization. In addition, the formulation in the spherical harmonic domain enables the flexible arrangement of microphones under the assumption of the spherical target region. Numerical simulation results indicated that high decomposition and reconstruction accuracies can be achieved by the proposed method, especially at low frequencies, with a low computational cost.
For transmission of a physical sound field in a large area, it is necessary to transform received signals of a microphone array into driving signals of a loudspeaker array to reproduce the sound ...field. We propose a method for transforming these signals by using planar or linear arrays of microphones and loudspeakers. A continuous transform equation is analytically derived based on the physical equation of wave propagation in the spatio-temporal frequency domain. By introducing spatial sampling, the uniquely determined transform filter, called a wave field reconstruction filter (WFR filter), is derived. Numerical simulations show that the WFR filter can achieve the same performance as that obtained using the conventional least squares (LS) method. However, since the proposed WFR filter is represented as a spatial convolution, it has many advantages in filter design, filter size, computational cost, and filter stability over the transform filter designed by the LS method.
We propose a useful formulation for ill-posed inverse problems in Hilbert spaces with nonlinear clipping effects. Ill-posed inverse problems are often formulated as optimization problems, and ...nonlinear clipping effects may cause nonconvexity or nondifferentiability of the objective functions in the case of commonly used regularized least squares. To overcome these difficulties, we present a tractable formulation in which the objective function is convex and differentiable with respect to optimization variables, on the basis of the Bregman divergence associated with the primitive function of the clipping function. By using this formulation in combination with the representer theorem, we need only to deal with a finite-dimensional, convex, and differentiable optimization problem, which can be solved by well-established algorithms. We also show two practical examples of inverse problems where our theory can be applied, estimation of band-limited signals and time-harmonic acoustic fields, and evaluate the validity of our theory by numerical simulations.
There is growing interest in new audio formats in the context of virtual reality (VR), and higher-order ambisonics (HOA) is preferred for VR systems to transmit recorded scenes owing to its ...transmission efficiency and its flexibility to work with different loudspeaker setups. However, the conversion between another well-known format, i.e., object format, and the HOA format is not fully addressed in the literature. To address this issue, blind source separation in a spherical harmonic (SH) domain can be considered as the best way to extract objects in terms of efficiency, i.e., decoding HOA signals for separation can be omitted. A few authors attempted to extract objects from encoded HOA signals directly by using multichannel non-negative matrix factorization (MNMF), but these approaches either assume only far-field sources or do not take array characteristics into account, which make these methods difficult to use for VR in practical situations where singers or speakers often perform close to microphones. Furthermore, MNMF generally requires a huge computational cost, although dimensional reduction to the SH domain is performed. In this work, we also model near-field sources by estimating the model parameters of non-negative tensor factorization (NTF) in the SH domain assuming that microphone signals can be obtained with a rigid spherical array. We propose a masking scheme to exclude noisy evanescent regions in the SH domain from the NTF cost function. Evaluations show that our method outperforms existing methods devised for the HOA format and that our masking approach is effective in improving the separation quality.
A spatial active noise control (ANC) method based on the individual kernel interpolation of primary and secondary sound fields is proposed. Spatial ANC is aimed at cancelling unwanted primary noise ...within a continuous region by using multiple secondary sources and microphones. A method based on the kernel interpolation of a sound field makes it possible to attenuate noise over the target region with flexible array geometry. Furthermore, by using the kernel function with directional weighting, prior information on primary noise source directions can be taken into consideration. However, whereas the sound field to be interpolated is a superposition of primary and secondary sound fields, the directional weight for the primary noise source was applied to the total sound field in previous work; therefore, the performance improvement was limited. We propose a method of individually interpolating the primary and secondary sound fields and formulate a normalized least-mean-square algorithm based on this interpolation method. Experimental results indicate that the proposed method outperforms the method based on total kernel interpolation.
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