Multiscale Generalized Sparse Plane Wave Decomposition in the Spherical Harmonic Domain

Huseyin Hacihabiboglu

cs.SDOct 15, 2026

Multiscale Generalized Sparse Plane Wave Decomposition in the Spherical Harmonic Domain

Authors: Huseyin Hacihabiboglu

Organizations: Graduate School of Informatics, METU, Ankara, TR-06800, Türkiye

Abstract

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

Panel of Figure 1 — 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 $\Omega=0$ (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 $(\frac{\pi}{2},\frac{\pi}{2})$ and $(\frac{\pi}{2},\frac{3\pi}{2})$ , 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

\infty

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

\textrm{SNR}\geq 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.

Panel of Figure 10 — Fig. 9: Marginal means (with 95% CI) of F1-score, ECM, SAAE, LE, and log-runtime with respect to $L$ .

Spatial Audio

Spatial audio studies how sound is captured, represented, generated, and perceived with direction, distance, motion, and room acoustics.

See all 103 papers

Masked Wavelet Scattering Transform Neural Field for Sound Field Reconstruction
Jun 3, 2026Xinmeng Luan, Samuel A. Verburg, Efren Fernandez-Grande +1Wavelet Scattering Transforms
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
Spherical Harmonic Sliced Wasserstein Displacement Interpolation for Acoustic Source and Reflection Density Modeling
Sep 18, 2026Yuancheng LuoSpatial Audio Sliced Wasserstein Distance
NuSpace Audio Cambridge, MA, USA
ASAP: An Azimuth-Priority Strip-Based Search Approach to Planar Microphone Array DOA Estimation in 3D
Apr 28, 2026Ming Huang, Shuting Xu, Leying Yang +6Microphone Array Processing Direction-of-Arrival Estimation
Southern University of Science and Technology, Shenzhen, China · Institute of Science Tokyo, Japan

Jun 3, 2026J/K move · Enter open · S save

Masked Wavelet Scattering Transform Neural Field for Sound Field Reconstruction

Xinmeng Luan, Samuel A. Verburg, Efren Fernandez-Grande, Gary Scavone

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

Wavelet Scattering Transforms

Open paper AskPDF arXiv

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.

Abstract

Spatial Audio

Explore similar work

Masked Wavelet Scattering Transform Neural Field for Sound Field Reconstruction

Spherical Harmonic Sliced Wasserstein Displacement Interpolation for Acoustic Source and Reflection Density Modeling

ASAP: An Azimuth-Priority Strip-Based Search Approach to Planar Microphone Array DOA Estimation in 3D