A Unified SVD-Modal Solution for Sparse Sound Field Reconstruction with Hybrid Spherical-Linear Microphone Arrays

We propose a data-driven sparse recovery framework for hybrid spherical linear microphone arrays using singular value decomposition (SVD) of the transfer operator. The SVD yields orthogonal microphone and field modes, reducing to spherical harmonics (SH) in the SMA-only case, while incorporating LMAs introduces complementary modes beyond SH. Modal analysis reveals consistent divergence from SH across frequency, confirming the improved spatial selectivity. Experiments in reverberant conditions show reduced energy-map mismatch and angular error across frequency, distance, and source count, outperforming SMA-only and direct concatenation. The results demonstrate that SVD-modal processing provides a principled and unified treatment of hybrid arrays for robust sparse sound-field reconstruction.

Hierarchical Sparse Sound Field Reconstruction with Spherical and Linear Microphone Arrays

Spherical microphone arrays (SMAs) are widely used for sound field analysis, and sparse recovery (SR) techniques can significantly enhance their spatial resolution by modeling the sound field as a sparse superposition of dominant plane waves. However, the spatial resolution of SMAs is fundamentally limited by their spherical harmonic order, and their performance often degrades in reverberant environments. This paper proposes a two-stage SR framework with residue refinement that integrates observations from a central SMA and four surrounding linear microphone arrays (LMAs). The core idea is to exploit complementary spatial characteristics by treating the SMA as a primary estimator and the LMAs as a spatially complementary refiner. Simulation results demonstrate that the proposed SMA-LMA method significantly enhances spatial energy map reconstruction under varying reverberation conditions, compared to both SMA-only and direct one-step joint processing. These results demonstrate the effectiveness of the proposed framework in enhancing spatial fidelity and robustness in complex acoustic environments.