Spatially sparse sound source localization in an under-determined system by using a hybrid compressive sensing method.

Near-field Acoustical Holography is a powerful tool for sound source identification and sound field reconstruction. Generally, many microphone measurements are required to construct a source model that can span the whole sound source region while simultaneously avoiding measurement errors and ensuring a high spatial sampling rate. That type of measurement is economically costly and hard to perform in industrial environments. Motivated by the desire to be able to use a relatively small number of microphone measurements to reconstruct a sound field and to accurately identify sound source locations, an Equivalent Source Method (ESM) is considered here. In particular, the focus is on the combination of a monopole-distribution ESM and a relatively small number of microphone measurements, thus creating an under-determined system. Wideband Acoustical Holography and l1-norm Convex Optimization are introduced to solve this under-determined inverse problem. Based on the attributes of these two methods, a hybrid method combining the best features of each is proposed to identify sound source locations.