  This article presents a method for estimating and reconstructing the spatial
energy distribution pattern of natural speech, which is crucial for achieving
realistic vocal presence in virtual communication settings. The method
comprises two stages. First, recordings of speech captured by a real, static
microphone array are used to create an egocentric virtual array that tracks the
movement of the speaker over time. This virtual array is used to measure and
encode the high-resolution directivity pattern of the speech signal as it
evolves dynamically with natural speech and movement. In the second stage, the
encoded directivity representation is utilized to train a machine learning
model that can estimate the full, dynamic directivity pattern given a limited
set of speech signals, such as those recorded using the microphones on a
head-mounted display. Our results show that neural networks can accurately
estimate the full directivity pattern of natural, unconstrained speech from
limited information. The proposed method for estimating and reconstructing the
spatial energy distribution pattern of natural speech, along with the
evaluation of various machine learning models and training paradigms, provides
an important contribution to the development of realistic vocal presence in
virtual communication settings.
