Polynomial Matrix Eigenvalue Decomposition of Spherical Harmonics for Speech Enhancement

Speech enhancement algorithms using polynomial matrix eigenvalue decomposition (PEVD) have been shown to be effective for noisy and reverberant speech. However, these algorithms do not scale well in complexity with the number of channels used in the processing. For a spherical microphone array sampling an order-limited sound field, the spherical harmonics provide a compact representation of the microphone signals in the form of eigenbeams. We propose a PEVD algorithm that uses only the lower dimension eigenbeams for speech enhancement at a significantly lower computation cost. The proposed algorithm is shown to significantly reduce complexity while maintaining full performance. Informal listening examples have also indicated that the processing does not introduce any noticeable artefacts.