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.
In many situations, humans make decisions based on serially sampled information through the observation of visual stimuli. To quantify the critical information used by the observer in such dynamic ...decision making, we here applied a classification image (CI) analysis locked to the observer's reaction time (RT) in a simple detection task for a luminance target that gradually appeared in dynamic noise. We found that the response-locked CI shows a spatiotemporally biphasic weighting profile that peaked about 300 ms before the response, but this profile substantially varied depending on RT; positive weights dominated at short RTs and negative weights at long RTs. We show that these diverse results are explained by a simple perceptual decision mechanism that accumulates the output of the perceptual process as modelled by a spatiotemporal contrast detector. We discuss possible applications and the limitations of the response-locked CI analysis.
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.
In many situations, humans serially sample information from many locations in an image to make an appropriate decision about a visual target. Spatial attention and eye movements play a crucial role ...in this serial vision process. To investigate the effect of spatial attention in such dynamic decision making, we applied a classification image (CI) analysis locked to the observer's reaction time (RT). We asked human observers to detect as rapidly as possible a target whose contrast gradually increased on the left or right side of dynamic noise, with the presentation of a spatial cue. The analysis revealed a spatiotemporally biphasic profile of the CI which peaked at ~ 350 ms before the observer's response. We found that a valid cue presented at the target location shortened the RT and increased the overall amplitude of the CI, especially when the cue appeared 500-1250 ms before the observer's response. The results were quantitatively accounted for by a simple perceptual decision mechanism that accumulates the outputs of the spatiotemporal contrast detector, whose gain is increased by sustained attention to the cued location.
•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.
We propose an element selection method for high-dimensional data that is applicable to a wide range of optimization criteria in a unifying manner. Element selection is a fundamental technique for ...reducing dimensionality of high-dimensional data by simple operations without the use of scalar multiplication. Restorability is one of the commonly used criteria in element selection, and the element selection problem based on restorability is formulated as a minimization problem of a loss function representing the restoration error between the original data and the restored data. However, conventional methods are applicable only to a limited class of loss functions such as ℓ 2 norm loss. To enable the use of a wide variety of criteria, we reformulate the element selection problem as a nonconvex sparse optimization problem and derive the optimization algorithm based on Douglas-Rachford splitting method. The proposed algorithm is applicable to any loss function as long as its proximal operator is available, e.g., ℓ 1 norm loss and ℓ ∞ norm loss as well as ℓ 2 norm loss. We conducted numerical experiments using artificial and real data, and their results indicate that the above loss functions are successfully minimized by the proposed algorithm.
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.
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 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.
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.
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