Obtaining far-field spherical directivities of guitar amplifiers from arbitrarily shaped arrays using the Helmholtz equation least-squares method

Bellows, Samuel D.; Leishman, Timothy W.

doi:10.1121/2.0001410

Cited by 4 publications

(5 citation statements)

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“…The irregularity of the combined sampling positions over the sphere and the uneven sampling density precludes the use of spherical quadrature rules and requires a least-squares fit to the data. Additionally, the sparse sampling in the region 0 < À45°necessitates regularization to avoid spurious and non-physical radiation lobes [18,21].…”

Section: Regularized Interpolationmentioning

confidence: 99%

“…The weighting matrix W determines how strongly to penalize the magnitude of different terms appearing in a. The unweighted choice (W = I, "white noise" assumption) applied in [18,21] represents the case where all expansion coefficients should be penalized equally. This assumption is a reasonable choice when little is known about the problem.…”

Section: Comparison Of Weighting Matricesmentioning

confidence: 99%

“…This assumption is a reasonable choice when little is known about the problem. This weighting is successful at removing the large radiation lobe appearing in the polar gap region compared to the unregularized case [18,21].…”

Section: Comparison Of Weighting Matricesmentioning

confidence: 99%

“…Besides the weighting matrix W, the regularized leastsquares fit requires choice of k and N. Previous works either used a fixed value [20], ad-hoc determination [21], or L-curve analysis [18] to determine k. Typically, source geometry determined the choice for the truncation degree N [18,20]; previous works did not consider the relation between N and k. However, knowledge of the physical problem suggests at two-step approach to setting k and N.…”

Section: Hyper-parameter Tuningmentioning

confidence: 99%

“…Aussal et al [20] later applied a weighted Tikhonov regularization to HRTF interpolation using a fixed amount of regularization but over varying spherical harmonic expansion degrees. Regularized least-squares fits have also been applied to directivity measurements, such as for guitar amplifiers [21].…”

Section: Introductionmentioning

confidence: 99%

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Combining multiple sparse measurements with reference data regularization to create spherical directivities applied to voice data

Bellows,

Katz

2024

Acta Acust.

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Obtaining high-resolution, spherical phoneme-dependent directivities for voice radiation is beneficial for numerous acoustics applications. This work reports on a spherical interpolation method based on two interleaved measurements using a regularized least-squares fit with reference data. Maximizing the spherical correlation between previously reported results and measured data determines the regularization hyper-parameters to ensure physical solutions. While the resultant spherical directivity patterns show similarities to time-averaged results, distinct radiation characteristics appear, particularly in the range of 630 Hz to 2 kHz.

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Section: Regularized Interpolationmentioning

confidence: 99%

Section: Comparison Of Weighting Matricesmentioning

confidence: 99%

Section: Comparison Of Weighting Matricesmentioning

confidence: 99%

Section: Hyper-parameter Tuningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combining multiple sparse measurements with reference data regularization to create spherical directivities applied to voice data

Bellows,

Katz

2024

Acta Acust.

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Batch Substitution Calibration of a Mems Microphone Array : Impact of Sensor Performance Dispersion on Directivity Estimation

Hartenstein,

Ollivier,

Silva

et al. 2024

ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Using learned priors to regularize the Helmholtz equation least-squares method

Lobato,

Sottek,

Vorländer

2024

The Journal of the Acoustical Society of America

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The Helmholtz equation least-squares (HELS) method is a valuable tool for estimating equivalent sound sources of a radiating object. It solves an inverse problem by mapping measured pressures to a set of basis functions satisfying the Helmholtz equation in spherical coordinates. However, this problem is often ill-posed, necessitating additional regularization methods, in which often variations of Ridge or Lasso are used. These conventional methods do not explicitly consider the distribution underlying the source radiations (besides sparsity) and are often used in the context of obtaining only a point estimate, even in the presence of ambiguity in the data. In this work, we propose the use of empirical priors through a normalizing flow model to enhance the inversion results obtained with the HELS method. We first validate our approach using numerical data and subsequently demonstrate its superior performance in interpolating a measured violin directivity compared to Lasso and Ridge methods, even when optimal regularization parameters are selected.

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Obtaining far-field spherical directivities of guitar amplifiers from arbitrarily shaped arrays using the Helmholtz equation least-squares method

Cited by 4 publications

References 0 publications

Combining multiple sparse measurements with reference data regularization to create spherical directivities applied to voice data

Combining multiple sparse measurements with reference data regularization to create spherical directivities applied to voice data

Batch Substitution Calibration of a Mems Microphone Array : Impact of Sensor Performance Dispersion on Directivity Estimation

Using learned priors to regularize the Helmholtz equation least-squares method

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