Sensor placement for sound field reconstruction in enclosures.

Sampling spatio-temporal acoustic fields is a challenging problem since it demands a large number of sensors. Typically, to characterize the pressure field inside an enclosure, the number of measurements required increases linearly with frequency and cubically with volume, becoming an intractable problem for rooms of moderate size even at low and mid frequencies. Sparse representation techniques, such as Compressed Sensing, rely on the sparsity of natural signals in certain representation domain to drastically reduce the number of measurements needed to sample such signals. In this study, we optimize the placement of sensors inside an enclosure in order to reduce the measurements required for a given reconstruction accuracy. The proposed methodology selects a sparse set of sensor positions from predefined grid via the QR factorization of the sensing matrix. Numerical results show an effective reduction in the required number of measurements when their positions are optimized, in contrast to standard random positioning. Unlike the majority of existing approaches, we study the placement problem for wide-band acoustic fields.