Sound field reconstruction in a room using low-rank approximation of mode shapes: validation and application

Sound field reconstruction in rooms is a subject of high interest in the domain of acoustic research.At low frequencies, a thorough understanding of sound field distribution is the key to identifying im-balance and irregularities caused by the room which will eventually lead to the coloration of sounds.Traditionally, an accurate rendering of the sound field would require an impractically high numberof microphone measurements at multiple locations in the room. Our research tackles this issue byexploiting the sparsity in modal decomposition expression of the sound field with the use of low-rankapproximation technique to significantly reduce the number of measurements. We first benchmarkthe techniques on an existing non-rectangular room model in Finite Element Method simulation withdifferent room settings to validate the high robustness and accuracy of the framework. The evaluationgives accurate results as the reconstructed sound fields are in very good agreement with the simulationreference and the existence of mode shapes are accurately depicted. Finally, we also prove that theframework performs well in cases where the sound field is altered by placing several active low fre-quency absorbers inside the room. This shows that our framework can be further extended to assessthe performance of passive/active absorbers in the domain of room modes equalization.