Signal compaction using polynomial EVD for spherical array processing with applications

Multi-channel signals captured by spatially separated sensors often contain a high level of data redundancy. A compact signal representation enables more efficient storage and processing, which has been exploited for data compression, noise reduction, and speech and image coding. This article focuses on the compact representation of speech signals acquired by spherical microphone arrays. A polynomial matrix eigenvalue decomposition (PEVD) can spatially decorrelate signals over a range of time lags and is known to achieve optimum multi-channel data compaction. However, the complexity of PEVD algorithms scales at best cubically with the number of channel signals, e.g., the number of microphones comprised in a spherical array used for processing. In contrast, the spherical harmonic transform (SHT) provides a compact spatial representation of the 3-dimensional sound field measured by spherical microphone arrays, referred to as eigenbeam signals, at a cost that rises only quadratically with the number of microphones. Yet, the SHT's spatially orthogonal basis functions cannot completely decorrelate sound field components over a range of time lags. In this work, we propose to exploit the compact representation offered by the SHT to reduce the number of channels used for subsequent PEVD processing. In the proposed framework for signal representation, we show that the diagonality factor improves by up to 7 dB over the microphone signal representation with a significantly lower computation cost. Moreover, when applying this framework to speech enhancement and source separation, the proposed method improves metrics known as short-time objective intelligibility (STOI) and source-to-distortion ratio (SDR) by up to 0.2 and 20 dB, respectively.