CNN Models for Microphone Array Covariance Matrix Upsampling and Acoustic Imaging
Authors: Marianthi Adamopoulou, Parthasaarathy Sudarsanam, David Diaz-Guerra, Meng Jiang, Archontis Politis, Seyed Jalaleddin Mousavirad, Tuomas Virtanen, Jan Lundgren
Organizations: Dept. of Comp. and Elec. Engineering Mid Sweden University Sundsvall, Sweden · Audio Research Group, Tampere University Tampere, Finland
Acoustic imaging visualization is a core methodology in acoustics, enabling spatial analysis of sound sources and acoustic scenes. However, limited sensor availability in practical systems motivate approaches that enhance spatial resolution without increasing the hardware complexity. In this paper, we focus on upsampling virtually a tetrahedral 4-microphone array to a spherical 32-microphone array by estimating the covariance matrices of the channels employing deep learning techniques. Five neural network architectures are investigated for covariance upsampling for acoustic imaging using the real-world STARSS23 dataset. These models are developed to estimate a 32-microphone, time-frequency covariance matrix from a 4-microphone input covariance representation. The proposed architectures are based on 2D convolutional layers to capture the underlying spatial-spectral structure of covariance matrices, and are further enhanced with frequency dynamic convolution to model their frequency-dependent properties. The proposed architectures are evaluated in terms of root mean square error (RMSE) and using delay-and-sum beamforming acoustic imaging. Quantitative results show that all models outperform a random-guess baseline, which yields an RMSE of 0.548, with the best-performing architecture achieving an RMSE of 0.432. We analyze qualitatively the performance of the proposed models through beamforming heatmap visualizations derived from the 4-channel input covariance, the 32-channel ground truth, and the predicted 32-channel covariance matrices. These results demonstrate that covariance upsampling significantly enhances the effective performance of the 4-channel microphone array, producing sound maps that closely resemble those obtained with the 32-channel array.
Latent Acoustic Mapping (LAM) is a self-supervised learning method that generates high-resolution spherical acoustic maps from multichannel recordings without labelled data, matching supervised baselines on direction-of-arrival benchmarks. However, LAM degrades significantly with sparse 4-channel arrays, as the low-resolution cross-spectral matrix captures far less spatial information than the 32-channel inputs LAM was designed for. We benchmark a diverse set of upsampling architectures, spanning lightweight convolutional networks, iterative back-projection models, physics-informed networks, and generative adversarial approaches. We also study whether aligning these upsamplers with LAM by training them jointly or in different stages helps preserve the spatial structure that LAM depends on. Results show that the original full-resolution LAM is the strongest, that separately trained lightweight models are the most competitive learned approaches, and that representation alignment between the upsampler and LAM matters more than model complexity.
The Relative Transfer Matrix (ReTM), recently introduced as a generalization of the relative transfer function for multiple receivers and sources, shows promising performance when applied to speech enhancement in noisy environments. Estimating the ReTM of sound sources by exploiting the covariance matrices of multichannel recordings is highly beneficial for practical applications and, to date, remains the only proposed approach. This paper investigates deep learning-based ReTM estimation. We propose three novel supervised learning frameworks using time and short-time frequency transform domain convolutional networks, and a Long Short-Term Memory-based recurrent neural network. Experimental results demonstrate that the proposed models achieve more accurate estimation of the ReTM using five objective metrics compared to the covariance-based method. We also show the effectiveness of the proposed frameworks for speech enhancement, achieving performance on par with the baseline method.
The minimum variance distortionless response (MVDR) beamformer is widely used for multichannel speech enhancement due to strong noise suppression while preserving target signals. In practice, its performance is sensitive to microphone self-noise and array mismatches. Existing approaches typically rely on fixed, manually tuned WNG thresholds or diagonal loading, leading to suboptimal performance under unknown or time-varying acoustic conditions. This paper proposes a data-driven MVDR framework that adaptively estimates the WNG constraint using a deep neural network. The network jointly predicts a time-frequency noise mask for covariance estimation and a frequency-dependent WNG threshold, enabling dynamic robustness-directivity control. A differentiable robust MVDR layer is integrated into the framework, allowing end-to-end optimization. Experiments demonstrate consistent improvements in speech quality and intelligibility over conventional fixed-WNG MVDR methods.