Physics-informed convolutional neural network with bicubic spline interpolation for sound field estimation

A sound field estimation method based on a physics-informed convolutional neural network (PICNN) using spline interpolation is proposed. Most of the sound field estimation methods are based on wavefunction expansion, making the estimated function satisfy the Helmholtz equation. However, these methods rely only on physical properties; thus, they suffer from a significant deterioration of accuracy when the number of measurements is small. Recent learning-based methods based on neural networks have advantages in estimating from sparse measurements when training data are available. However, since physical properties are not taken into consideration, the estimated function can be a physically infeasible solution. We propose the application of PICNN to the sound field estimation problem by using a loss function that penalizes deviation from the Helmholtz equation. Since the output of CNN is a spatially discretized pressure distribution, it is difficult to directly evaluate the Helmholtz-equation loss function. Therefore, we incorporate bicubic spline interpolation in the PICNN framework. Experimental results indicated that accurate and physically feasible estimation from sparse measurements can be achieved with the proposed method.

Region-to-region kernel interpolation of acoustic transfer function with directional weighting

A method of interpolating the acoustic transfer function (ATF) between regions that takes into account both the physical properties of the ATF and the directionality of region configurations is proposed. Most spatial ATF interpolation methods are limited to estimation in the region of receivers. A kernel method for region-to-region ATF interpolation makes it possible to estimate the ATFs for both source and receiver regions from a discrete set of ATF measurements. We newly formulate the reproducing kernel Hilbert space and associated kernel function incorporating directional weight to enhance the interpolation accuracy. We also investigate hyperparameter optimization methods for this kernel function. Numerical experiments indicate that the proposed method outperforms the method without the use of directional weighting.

Spatial active noise control based on individual kernel interpolation of primary and secondary sound fields

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.

Mean-square-error-based secondary source placement in sound field synthesis with prior information on desired field

A method of optimizing secondary source placement in sound field synthesis is proposed. Such an optimization method will be useful when the allowable placement region and available number of loudspeakers are limited. We formulate a mean-square-error-based cost function, incorporating the statistical properties of possible desired sound fields, for general linear-least-squares-based sound field synthesis methods, including pressure matching and (weighted) mode matching, whereas most of the current methods are applicable only to the pressure-matching method. An efficient greedy algorithm for minimizing the proposed cost function is also derived. Numerical experiments indicated that a high reproduction accuracy can be achieved by the placement optimized by the proposed method compared with the empirically used regular placement.

Sound Field Reproduction With Weighted Mode Matching and Infinite-Dimensional Harmonic Analysis: An Experimental Evaluation

Sound field reproduction methods based on numerical optimization, which aim to minimize the error between synthesized and desired sound fields, are useful in many practical scenarios because of their flexibility in the array geometry of loudspeakers. However, the reproduction performance of these methods in a practical environment has not been sufficiently investigated. We evaluate weighted mode matching, which is a sound field reproduction method based on the spherical wavefunction expansion of the sound field, in comparison with conventional pressure matching. We also introduce a method of infinite-dimensional harmonic analysis for estimating the expansion coefficients of the sound field from microphone measurements. Experimental results indicated that weighted mode matching using the expansion coefficients of the transfer functions estimated by the infinite-dimensional harmonic analysis outperforms conventional pressure matching, especially when the number of microphones is small.

Kernel Learning For Sound Field Estimation With L1 and L2 Regularizations

A method to estimate an acoustic field from discrete microphone measurements is proposed. A kernel-interpolation-based method using the kernel function formulated for sound field interpolation has been used in various applications. The kernel function with directional weighting makes it possible to incorporate prior information on source directions to improve estimation accuracy. However, in prior studies, parameters for directional weighting have been empirically determined. We propose a method to optimize these parameters using observation values, which is particularly useful when prior information on source directions is uncertain. The proposed algorithm is based on discretization of the parameters and representation of the kernel function as a weighted sum of sub-kernels. Two types of regularization for the weights, $L_1$ and $L_2$, are investigated. Experimental results indicate that the proposed method achieves higher estimation accuracy than the method without kernel learning.

Binaural rendering from microphone array signals of arbitrary geometry

A method of binaural rendering from microphone array signals of arbitrary geometry is proposed. To reproduce binaural signals from microphone array recordings at a remote location, a spherical microphone array is generally used for capturing a soundfield. However, owing to the lack of flexibility in the microphone arrangement, the single spherical array is sometimes impractical for estimating a large region of a soundfield. We propose a method based on harmonic analysis of infinite order, which allows the use of arbitrarily placed microphones. In the synthesis of the estimated soundfield, a spherical-wave-decomposition-based binaural rendering is also formulated to take into consideration the distance in measuring head-related transfer functions. We develop and evaluate a composite microphone array consisting of multiple small arrays. Experimental results including those of listening tests indicate that our proposed method is robust against change in listening position in the recording area.

MeshRIR: A Dataset of Room Impulse Responses on Meshed Grid Points For Evaluating Sound Field Analysis and Synthesis Methods

A new impulse response (IR) dataset called "MeshRIR" is introduced. Currently available datasets usually include IRs at an array of microphones from several source positions under various room conditions, which are basically designed for evaluating speech enhancement and distant speech recognition methods. On the other hand, methods of estimating or controlling spatial sound fields have been extensively investigated in recent years; however, the current IR datasets are not applicable to validating and comparing these methods because of the low spatial resolution of measurement points. MeshRIR consists of IRs measured at positions obtained by finely discretizing a spatial region. Two subdatasets are currently available: one consists of IRs in a three-dimensional cuboidal region from a single source, and the other consists of IRs in a two-dimensional square region from an array of 32 sources. Therefore, MeshRIR is suitable for evaluating sound field analysis and synthesis methods. This dataset is freely available at \url{https://sh01k.github.io/MeshRIR/} with some codes of sample applications.