Sound Field Reconstruction for an Under-Determined System and its Application

Near-Field Acoustical Holography (NAH) is an inverse process in which sound pressure measurements made in the near-field of an unknown sound source can be used to reconstruct the sound field so that source locations can be identified. Usually a large number of measurements is required for the usual NAH methods since a large number of parameters in the source or field model need to be determined. However, a large-scale microphone measurement is costly and hard to perform, so the use of NAH is limited by practical experimental conditions. In the present work, with the motivation of decreasing the number of microphone measurements required, and thus facilitating the measurement process, two sparse Equivalent Source Method (ESM) algorithms were studied: i.e., Wideband Acoustical Holography (WBH) and l_1-norm minimization. Based on these two algorithms, a new hybrid NAH procedure was proposed and demonstrated. To study and verify the above mentioned algorithms, simulations of different sources were conducted and then experiments were conducted on different sources: i.e., a loudspeaker cabinet and a diesel engine.