A Compressed Equivalent Source Method Based on Equivalent Redundant Dictionary for Sound Field Reconstruction

Abstract

The equivalent source method (ESM) based on compressive sensing (CS) requires that the source has a sparse or approximately sparse representation in a suitable basis or dictionary. However, in practical applications, it is not easy to find the appropriate basis or dictionary due to the indeterminate characteristics of the source. To solve this problem, an equivalent redundant dictionary is constructed, which contains two core parts: one is the equivalent dictionary used in the CS-based ESMs under the sparse assumption, and the other one is the orthogonal basis obtained by the singular value decomposition (SVD). On this foundation, a method named compressed ESM based on the equivalent redundant dictionary (ERDCESM) is proposed to enhance the performances of source field reconstruction for different types of sources. Moreover, inspired by the idea of functional beamforming (FB), ERDCESM with order v (ERDCESM- v ) can possess a high dynamic range when detecting the source location. The numerical simulations are carried out at different frequencies to evaluate the performance of the proposed method, and the results suggest that the proposed method performs well both for sparse and even spatially extended sources. The validity and practicality of the proposed method are also verified by the experimental results.