Sparse plane wave decomposition (SPWD) is a physics-driven model-based approach for analyzing sound fields that is suitable for real-time operation. SPWD is used in different contexts such as direction of arrival (DOA) estimation and sound field separation. SPWD employs spherical Dirichlet kernels to decompose sound fields represented as steered response maps into a finite number of plane waves using sparse recovery techniques. This article proposes a multiscale generalized sparse plane wave decomposition approach that uses an optimal spherical kernel and a multiscale sparse decomposition method to improve recovery performance. The utility of the proposed approach is shown by comparisons with the original SPWD approach via extensive numerical simulations.
Figures & tables
Fig. 1: The spherical Dirichlet kernel (blue) and the proposed generalized spherical kernel (orange) for different orders, N=1 to N=6 , i.e. (a)-(f), in dB. The maximum corresponds to Ω=0 (i.e. the axis of symmetry).
Fig. 2: Comparison of SRF and GSRF of order N=6 for two plane waves of amplitudes 1.0 and −0.14 incident from (2π,2π) and (2π,23π) , respectively. Mollweide projection is used in the plots.
Fig. 3: F1-scores for different methods and number of sources. Only the conditions for N=2 , N=4 and N=6 are shown at 10 , 20 , 30 , 40 and ∞ dB SNR. The curves represent the mean values and shaded areas represent one standard deviation above and below the mean.
Fig. 4: Average F1-scores for different methods at different SH orders showing single SPWD (red diamonds), single GSPWD (green triangles), multiscale SPWD (orange squares), and multiscale GSPWD (blue circles). N=1 for which multiscale versions collapse into their single scale versions is indicated by gray shading.
N
Comparison
Estimate
t(490)
p
Cohen’s d
4
SPWD (Multiscale)
0.003
0.625
1.000
0.030
GSPWD (Single)
0.018
3.399
0.004
0.180
SPWD (Single)
0.006
0.990
1.000
0.058
5
SPWD (Multiscale)
0.020
4.329
<.001
0.194
GSPWD (Single)
0.064
10.895
<.001
0.616
SPWD (Single)
0.090
14.722
<.001
0.861
TABLE I: Post-hoc comparisons of F1-score (Multiscale GSPWD − Other Method) at N=4 , 5 , and 6 for SNR≥20 dB. p -values are Bonferroni-corrected within each SH order.
Fig. 5: Event Count Mismatch (ECM) for different methods and SNR levels. The curves represent the mean values and shaded areas represent the 95% CI above and below the mean. N=1 for which multiscale versions collapse into their single scale versions is indicated by gray shading.
Fig. 6: Event Count Mismatch (ECM) Rate (top row) and ECM Magnitude (bottom row) for different methods and SNR levels. 95% CIs for Mean ECM Magnitudes are also shown for each noise level. N=1 for which multiscale versions collapse into their single scale versions is indicated by gray shading.
Fig. 7: Support-aware Amplitude Error (SAAE) for different methods, SNR levels and SH orders. N=1 for which multiscale versions collapse into their single scale versions is indicated by gray shading.
Fig. 8: Localization Error (LE) in degrees for different methods and number of sources. Only the conditions for N=2 , N=4 and N=6 are shown for conciseness. The curves represent the mean values and shaded areas represent one standard deviation above and below the mean.
Fig. 9: Marginal means (with 95% CI) of F1-score, ECM, SAAE, LE, and log-runtime with respect to L .
In this paper, we propose a reconstruction framework that leverages the Wavelet Scattering Transform (WST) as a multi-scale feature extractor to impose statistical priors under sparse observation conditions. The reconstruction problem is formulated as an optimization task and solved using a neural field, with the WST incorporated into the training loss function. As a proof of concept, we validate the proposed method on HRTF upsampling. A masking strategy is applied to the WST coefficients, resulting in a two-phase procedure. The first phase learns a binary mask from a small multi-subject dataset, while the second phase applies the learned mask to the WST coefficients of an individual HRTF to preserve informative statistical structures during reconstruction. Validation against baseline methods, which also serve as an ablation study of the different components of the framework, demonstrates the effectiveness of the proposed approach.
Xinmeng Luan, Samuel A. Verburg, Efren Fernandez-Grande +1
Schulich School of Music, McGill University, CIRMMT† Montreal, Canada · Dept. of Electrical and Photonics Engineering, Technical University of Denmark Kgs. Lyngby, Denmark · Dept. of Audiovisual Engineering and Communications, Universidad Politécnica de Madrid Madrid, Spain
Spatial room impulse responses (SRIRs) capture directional distributions of acoustic sound-sources and their reflections. However, collecting SRIRs of moving sound-sources remains a challenge, requiring complex interpolations across measurements that account for multi-path spatial-temporal dynamics. This paper investigates the Wasserstein metric and displacement for evaluating interpolated SRIR echo densities in the spherical harmonic domain. We present novel sum-of-magnitude square expansions for efficiently fitting probability density functions, maximizing likelihood, inverse sampling, and computing spherical sliced Wasserstein interpolations. Experiments compare the Wasserstein displacements and metric to linear and geometric interpolations of SRIR image-source densities on a line-path, and demonstrate model-order reduction.
Direction-of-arrival (DOA) estimation is an important task in microphone array processing and many downstream applications. The steered response power with phase transform (SRP-PHAT) method has been widely adopted for DOA estimation in recent years. However, accurate SRP-PHAT estimation in 3D scenarios requires evaluating steering responses over thousands of candidate directions, severely limiting real-time performance on resource-constrained platforms. This challenge becomes even more critical for planar arrays, which are widely used in robotics due to their structural simplicity. Motivated by the fact that azimuth estimation is usually more reliable than elevation estimation for most arrays, we propose ASAP, an azimuth-priority strip-based search approach to planar microphone array DOA estimation in 3D. In the first stage, ASAP performs coarse-to-fine region contraction within azimuthal strips to lock azimuth angles while retaining multiple maxima through spherical caps. In the second stage, it refines elevation along the great-circle arc between two close candidates. Extensive simulations and real-world experiments validate the efficiency and merits of the proposed method over existing approaches.
Ming Huang, Shuting Xu, Leying Yang +6
Southern University of Science and Technology, Shenzhen, China · Institute of Science Tokyo, Japan