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.
Highlights
The equivalent source method (ESM) based on Nearfield acoustic holography (NAH) is a powerful tool for identifying sound sources and visualizing sound fields [1,2,3]
The sound pressure on the reconstruction plane can be expressed as Equation (10): PR = DΥ. In this equivalent redundant dictionary D, φ is the equivalent dictionary used in compressive ESM (CESM), which is especially suitable for the sources distributed spatially sparse
When the source satisfactory because, for the source that distributed sparsely in the space domain, its spatial acoustic was set at 2000 Hz, a similar conclusion could be derived that CESM and ERDCESM produced a better modes were spatially continuous rather than sparse
Summary
The equivalent source method (ESM) based on Nearfield acoustic holography (NAH) is a powerful tool for identifying sound sources and visualizing sound fields [1,2,3]. When the source is not distributed sparsely (e.g., the spatially extended source), it is necessary to construct an appropriate basis or dictionary to sparsely decompose the sound field so that the sparsity condition required by the CS theory can be fulfilled. In this case, two typical methods, named the total generalized variation regularization (TGV) [22] and the compressed modal equivalent point source method (CMESM) [23], are introduced. A compressed ESM based on an equivalent redundant dictionary (ERDCESM) is proposed, which is applicable both for sparse and even spatially extended sources.
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