Signal reconstruction from its mel-spectrogram is known as mel-spectrogram inversion and has many applications, including speech and foley sound synthesis. In this paper, we propose a mel-spectrogram inversion method based on a rigorous optimization algorithm. To reconstruct a time-domain signal with inverse short-time Fourier transform (STFT), both full-band STFT magnitude and phase should be predicted from a given mel-spectrogram. Their joint estimation has outperformed the cascaded full-band magnitude prediction and phase reconstruction by preventing error accumulation. However, the existing joint estimation method requires many iterations, and there remains room for performance improvement. We present an alternating direction method of multipliers (ADMM)-based joint estimation method motivated by its success in various nonconvex optimization problems including phase reconstruction. An efficient update of each variable is derived by exploiting the conditional independence among the variables. Our experiments demonstrate the effectiveness of the proposed method on speech and foley sounds.

Element selection techniques for high-dimensional features have various applications in machine learning. In general, the problem of element selection is typically solved by greedy methods or convex relaxation methods. However, these algorithms are applicable to only a specific class of optimization criteria such as the minimization of the squared error loss between the original and restored data. To overcome this limitation, we propose an element selection algorithm based on non-convex sparse optimization that can be used with a wider class of optimization criteria than conventional algorithms. In the proposed method, an algorithm based on the alternating direction method of multipliers (ADMM) is de-rived by reformulating the element selection problem as a matrix optimization on a non-convex set. A numerical experiment demonstrated the effectiveness of the proposed method for element selection with a non-squared error loss compared with the conventional greedy method.

A multizone sound field control method, called amplitude matching, is proposed. The objective of amplitude matching is to synthesize a desired amplitude (or magnitude) distribution over a target region with multiple loudspeakers, whereas the phase distribution is arbitrary. Most of the current multizone sound field control methods are intended to synthesize a specific sound field including phase or to control acoustic potential energy inside the target region. In amplitude matching, a specific desired amplitude distribution can be set, ignoring sound propagation directions. Although the optimization problem of amplitude matching does not have a closed-form solution, our proposed algorithm based on the alternating direction method of multipliers (ADMM) allows us to accurately and efficiently synthesize the desired amplitude distribution. We also introduce the differential-norm penalty for a time-domain filter design with a small filter length. The experimental results indicated that the proposed method outperforms current multizone sound field control methods in terms of accuracy of the synthesized amplitude distribution.

Linear dimensionality reduction of signals observed by a sensor array is often useful in balancing the accuracy and speed of post-stage processing, especially in real-time systems with limited computational resources. However, for multichannel time-series signals having time-invariant intertemporal and interchannel correlations, the direct application of frequency-wise linear dimensionality reduction method requires a large number of digital filters with large filter lengths, which is still unpreferable in the viewpoint of computational cost. We propose a frequency-independent, i.e., instantaneous, linear dimensionality reduction method that achieves low computational cost and latency and high restoration accuracy. We also show several results of numerical experiments to compare the proposed method with other instantaneous linear dimensionality reduction methods, i.e., the principal component analysis and element selection method, and demonstrate the effectiveness of the proposed method.

A method to interpolate the acoustic transfer function (ATF) between regions using kernel ridge regression (KRR) is proposed. Conventionally, the ATF interpolation problem is strongly restricted and situational, depending on knowledge of environmental conditions while not accounting for source position variation. We derive our interpolation function as the solution of an optimization problem defined on a function space where every element holds the acoustic properties of the ATF. By making the space a reproducing kernel Hilbert space (RKHS), we can guarantee that our problem has a known and unique optimizer. The generality of the formulation of this method enables region-to-region estimations, with variable source and receiver within the assigned bounds. The definition of a RKHS also allows for the use of kernel principal component analysis, thereby efficiently providing greater noise robustness to our interpolation function. Our proposed method is compared with a previously established region-to-region interpolation method in numerical simulations where the advantages of the KRR approach are confirmed, showing lower error and greater stability for higher frequencies.

A sound field control method for synthesizing a desired amplitude distribution inside a target region, amplitude matching, is proposed. In the conventional pressure matching, a desired sound field is set as a pressure distribution including amplitude and phase. In personal audio applications, it is sometimes not necessary to synthesize a specific phase distribution, but a certain acoustic power level should be controlled inside the target region. Since the optimization problem to achieve amplitude matching becomes nonlinear, there is no closed-form solution and numerical optimization algorithms are generally applied. We derive an efficient algorithm for the amplitude matching based on the majorization–minimization algorithm. Numerical experiments indicated that high control accuracy over the target region can be achieved with low computational cost by using the proposed algorithm.

An active noise control (ANC) method to reduce noise over a region in space based on kernel interpolation of sound field is proposed. Current methods of spatial ANC are largely based on spherical or circular harmonic expansion of the sound field, where the geometry of the error microphone array is restricted to a simple one such as a sphere or circle. We instead apply the kernel interpolation method, which allows for the estimation of a sound field in a continuous region with flexible array configurations. The interpolation scheme is used to derive adaptive filtering algorithms for minimizing the acoustic potential energy inside a target region. A practical time-domain algorithm is also developed together with its computationally efficient block-based equivalent. We conduct experiments to investigate the achievable level of noise reduction in a two-dimensional free space, as well as adaptive broadband noise control in a three-dimensional reverberant space. The experimental results indicated that the proposed method outperforms the multipoint-pressure-control-based method in terms of regional noise reduction.

A sensor (microphone) placement method based on mutual information for spatial sound field recording is proposed. The sound field recording methods using distributed sensors enable the estimation of the sound field inside a target region of arbitrary shape; however, it is a difficult task to find the best placement of sensors. We focus on the mutual-information-based sensor placement method in which spatial phenomena are modeled as a Gaussian process (GP). We propose the use of the sound-field-interpolation kernel for the covariance of measurements in a GP model to obtain the sensor placement suitable for sound field recording. We also extend the method to treat broadband signals and derive an efficient algorithm based on block matrix inversion. Numerical simulation results indicated that the proposed method achieves accurate sound field estimation compared with a method using the generally used Gaussian kernel.

A spatial active noise control (ANC) method taking prior information on the approximate direction of primary noise sources into consideration is proposed. ANC aims to cancel incoming primary noise using secondary loudspeakers. Conventional multipoint ANC does not guarantee the reduction of noise between multiple discrete control points; therefore, several attempts have been made to reduce the noise over an entire target region, i.e., by spatial ANC. We have recently proposed a spatial ANC method based on kernel ridge regression for sound field interpolation using distributed microphones and loudspeakers, where the cost function is formulated on the basis of the regional power obtained by kernel interpolation. In this study, we incorporate prior knowledge on the noise source direction into spatial ANC based on the kernel interpolation with directional weighting. Numerical simulation results indicate that the proposed method can achieve larger regional noise reduction than the methods without the information on noise source direction.

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.

A method for feedforward active noise control (ANC) over a spatial region is proposed. Conventional multipoint ANC aims to reduce the noise at multiple discrete positions; therefore, the noise reduction in the region between these points cannot be guaranteed. Recent studies revealed the possibility of spatial ANC, i.e., noise control in a continuous target region. These methods are essentially based on spherical/circular harmonic decomposition of the sound field by using spherical/circular arrays and have mainly been investigated for feedback control under the assumption of periodicity of the noise. We apply a sound field interpolation method based on kernel ridge regression to feedforward spatial ANC to control spatial nonstationary noise using distributed arrays. Numerical simulation results indicated that a large regional noise reduction is achieved by the proposed method compared with feedforward multipoint ANC.

A sound field reconstruction method for a region including sources is proposed. Under the assumption of spatial sparsity of the sources, this reconstruction problem has been solved by using sparse decomposition algorithms with the discretization of the target region. Since this discretization leads to the off-grid problem, we previously proposed a gridless sound field decomposition method based on the reciprocity gap functional in the spherical harmonic domain. Even though this method allows efficient estimation with a closed-form solution while avoiding the off-grid problem, the estimation using a single time-frequency bin can be greatly affected by measurement errors. We formulate an optimization problem using the identical structure of source locations in multiple time-frequency bins and derive an algorithm based on an annihilating filter. Numerical simulation results indicated that robustness against noise can be improved by the proposed method.

A sound field reproduction method based on the spherical wavefunction expansion of sound fields is proposed, which can be flexibly applied to various array geometries and directivities. First, we formulate sound field synthesis as a minimization problem of some norm on the difference between the desired and synthesized sound fields, and then the optimal driving signals are derived by using the spherical wavefunction expansion of the sound fields. This formulation is closely related to the mode-matching method; a major advantage of the proposed method is the optimal weight on the mode determined according to the norm to be minimized instead of the empirical truncation in the mode-matching method. We also provide some examples of norms and their corresponding weights in analytical forms. Both interior and exterior sound field reproduction are considered in the proposed method, and some applications, such as multizone reproduction and interior reproduction with exterior cancellation, are also discussed. Numerical simulation results indicated that higher reproduction accuracy can be achieved by the proposed method than by the current pressure-matching and mode-matching methods.

A method for sound field reproduction with the suppression of exterior radiation is proposed, which makes it possible to synthesize a desired sound field in a reverberant environment without prior knowledge of the transfer functions of the multiple loudspeakers. The objective function used to achieve this is formulated as the weighted sum of the interior reproduction error and exterior radiation power. The optimal driving signals are derived by harmonic expansion of both the interior and exterior sound fields. In contrast to the empirical coefficient truncation in the state of the art, in the proposed method, an optimal weighting of the harmonic coefficients is derived analytically. Numerical simulation results indicated that high interior reproduction accuracy and exterior power suppression can be achieved by the proposed method compared with the mode-matching method using harmonic-order truncation owing to the optimal weighting.

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 sound field reproduction method that exploits prior information on listening areas is proposed. Most current methods are aimed at reproducing the sound field over the entire space or around listener locations. We formulate the objective function for this problem as the expectation minimization of the spatial squared error of the sound pressure inside the listening areas. The optimal driving signals are obtained by circular harmonic expansion. Comparing the proposed method with the mode-matching method, the advantage of the proposed method appears in the optimal weighting matrix of the circular harmonics, which depends on the location and range of the listening area. Numerical simulations indicated that high reproduction accuracy compared with other current methods can be maintained in the listening areas at high frequencies by using the proposed method.