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.