Machine Learning Assisted Signal Enhancement
Authors:   , Yan Longfei 
Published: March 2024

<p><strong>In an era of abundant signals, the ability to obtain desired signals while rejecting undesired ones has become increasingly crucial. Often, the desired signals are mixed with interference or contaminated by noise. Signal enhancement techniques play a vital role in performing tasks such as signal separation, extraction, and suppression. This thesis addresses critical challenges in signal enhancement tasks by harnessing the power of machine learning techniques.</strong></p><p>Firstly, we propose a novel independence criterion called the Finite Basis Independence Criterion (FBIC). This criterion estimates the Hirschfeld-Gebelein-Rényi maximum correlation coefficient between tested variables and is based on mapping functions from a subspace of finite basis. FBIC detects dependence between variables in linear time and outperforms more computationally expensive kernel-based counterparts. Extensive testing in Independent Component Analysis benchmarks demonstrates its potential for various signal separation applications.</p><p>Secondly, we conduct a comprehensive robustness analysis of a popular signal enhancement approach: fixed beamforming based on first-order linear Differential Microphone Arrays (DMAs). We demonstrate that both bounded and unbounded phase errors of microphones can affect the mainlobe orientation of the beamformer. Analytically derived white noise gain thresholds indicate when mainlobe misorientation occurs. Through rigorous mathematical derivations, we prove that a higher number of microphones and increased spacing between microphones contribute to the robustness of the beamformer. This work provides practical guidelines for designing robust first-order linear DMAs.</p><p>Thirdly, we propose a neural network model to optimize both the geometry and spatial filter of linear DMAs. The model consists of two feed forward neural networks and is trained end-to-end. The signals enhanced by this model exhibit superior quality compared to those obtained from conventional DMA approaches. Furthermore, the model offers flexibility in controlling the tradeoff between different performance metrics, allowing for customized optimization.</p><p>Lastly, we extend the neural network model to a general framework that allows optimization of microphone arrays of any geometry, along with their spatial filters. This model employs ResNets and augmented Lagrangian techniques to achieve state-of-the-art frequency-invariant fixed beamforming performance. We showcase our performance in linear, circular, and concentric circular microphone arrays. Moreover, our findings challenge the conventional belief that concentric circular arrays require multiple rings, as we demonstrate that good performance can be achieved with only one ring.</p><p>Overall, this thesis contributes novel techniques and insights to the field of signal enhancement, leveraging machine learning approaches to address key challenges. The proposed criteria, guidelines and models have the potential to advance various signal separation applications and enhance the overall quality of processed signals.</p>