Research on SONAH calculation accuracy optimization based on sparse matrix

Abstract

This study proposes an enhanced Statistically Optimized Near-field Acoustic Holography that integrates sparse matrix technique to address the longstanding challenge of low-frequency reconstruction accuracy. Conventional SONAH, while efficient and widely used, suffers from high condition numbers and numerical instability at low frequencies due to the smooth variation of sound pressure and dense propagation matrices. By leveraging the inherent sparsity in the propagation and reconstruction matrices, the proposed approach significantly improves numerical stability. The method is validated through both numerical simulations and field experiments conducted in a fully anechoic chamber using a scanning microphone array. Simulation results show that the sparse matrix-based algorithm achieves a notable reduction in average reconstruction error within the 100–500 Hz octave bands, outperforming the conventional SONAH by an average of 3.3 dB. Furthermore, field experiment results confirm the superior performance of the proposed algorithm, with an overall average reconstruction error that is 7.3 dB lower than that of the traditional approach. In addition to its accuracy advantages, the sparse matrix-based algorithm also demonstrates improved computational efficiency, utilizing approximately 20 % of the CPU resources, in contrast to the 60 % consumed by the conventional SONAH. This represents a reduction of two-thirds in CPU usage, highlighting the improved computational efficiency of the proposed approach. Given its compatibility with a wide range of measurement configurations and its enhanced performance in low-frequency reconstruction, the proposed method shows promise for practical applications such as mechanical fault diagnosis and architectural acoustic analysis. Further validation using high-channel-count and irregular array configurations is expected to extend its applicability to more complex field scenarios. Overall, this work highlights the potential of sparse matrix integration to enhance SONAH and offers new insights for effective sound field reconstruction in complex acoustic environments.