Sparse Recovery and Ray Space

Abstract

In the age of informatization and digitalization, it is extremely important to exchange

information between reality and the digital world. Numerous interfaces exist to capture human

outputs, such as keyboards, mice, and touch screens designed for hand gestures, along with

cameras for images and, importantly, microphones for sound. As microphones and microphone

arrays become more ubiquitous in everyday life, the study and improvement of microphone

array signal processing is increasingly significant. Array beamforming, a key technique in this

field, allows for directional sensitivity and the enhancement of target sounds, while suppressing

unwanted noise, making it essential for applications like speech recognition, acoustic source

localization, and noise reduction. This thesis, therefore, focuses on advancing array

beamforming methods and other techniques to fully realize the potential of microphone arrays.

The methods of Sparse Recovery (SR) and Ray Space (RS) are two advantageous approaches

in array signal processing. Sparse Recovery interprets the sound field with the fewest necessary

sound sources, a principle that has been explored with spherical microphone arrays by the

Computational Audio Research Laboratory at the University of Sydney. This thesis extends SR

by applying it to linear microphone arrays, which provide unique benefits for perceiving near-

field sound and separating sources over varying distances. Ray Space, meanwhile, enables

sound field sensing from multiple distributed microphone arrays, with each array acting as a

viewpoint. By synthesizing SR and RS, this thesis aims to improve spatial resolution, signal-to-

noise ratio, and overall accuracy in sound field analysis.