Recovering phase relationships between non-synchronous microphone array measurements
Résumé
In acoustic reconstruction, the frequency range is fundamentally determined by the size of the array and
the microphone density. A solution to achieve large array and/or high microphone density is to scan the
object of interest by moving sequentially a small prototype array (sequential measurements). In comparison
with a large array and/or high microphone density array that can acquire simultaneously all the information
of the spectral matrix (including both the auto-spectral and cross-spectral parts), sequential measurements
can only acquire a block diagonal spectral matrix that comprises auto-spectra of each measurement, while
the cross-spectra between sequential measurement remain unknown due to the missing phase relationships
between consecutive array positions. Nevertheless, this unknown cross-spectral parts are significant for a-
coustic reconstruction. Thus, the problem is formulated as a spectral matrix completion problem, i.e. how to
reconstruct a complete matrix by incomplete measurements? This typically requires a number of fixed refer-
ences in classic methods (Conditioned Spectral Analysis, Principal Component Analysis). In this work, the
case of sequential measurements without reference is dealt with, boiling down the spectral matrix completion
problem to rank minimization and spatial basis projection. Subsequently, a cyclic projection(CP) algorithm
is proposed in this work to find an optimal solution in the intersection between three predefined sets