Reconstruction of the sound field in a room using compressive sensing

Capturing the impulse or frequency response functions within extended regions of a room requires an unfeasible number of measurements. In this study, a method to reconstruct the response at arbitrary points based on compressive sensing (CS) is examined. The sound field is expanded into plane waves and their amplitudes are estimated via CS, obtaining a spatially sparse representation of the sound field. The validity of the CS assumptions are discussed, namely, the assumption of the wave field spatial sparsity (which depends strongly on the properties of the specific room), and the coherence of the sensing matrix due to different spatial sampling schemes. An experimental study is presented in order to analyze the accuracy of the reconstruction. Measurements with a scanning robotic arm make it possible to circumvent uncertainty due to positioning and transducer mismatch, and examine the accuracy of the reconstruction over extended regions of space. The results indicate that near perfect reconstructions are possible at low frequencies, even from a limited set of measurements. In addition, the study shows that it is possible to reconstruct damped room responses with reasonable accuracy well into the mid-frequency range.