Acoustic Imaging by the Non-Synchronous Measurements with Perfect Overlapping

The conventional approaches to source reconstruction follow the fundamental limitation of the aperture of the array and the microphone density owing to expenditure and technical reasons, which aroused the problem of reducing the number of microphones. Nevertheless, one rudimental problem is simultaneously raised when the problem of reducing the number of microphones is conceived, which is explicated by what is the minimum number of microphones that should be used for the purpose of certificating the reconstruction performance. In this paper, the acoustic source reconstruction is viewed with a statistical learning perspective firstly, which brings in the minimum number of microphones in simultaneous measurements setup. Secondly, the problem of reducing the number of microphones is boiled down to rank minimisation in sequential measurements, which eludes the 'overweening sparse' phenomenon caused by the $L0$ minimisation in the acoustic source reconstruction scenario with the reduced number of microphones.