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.

Compressive equivalent source method based on particle velocity measurements for near-field acoustic holography

“…However, this paper mainly focuses on the simple and compact sound source, and the sound source is assumed in the free sound field environment. For the complicated sound source or the spatially distributed sound sources, or the practical non-free sound field, there are still a lot of work to be done, such as the elaborate construction of the sparse basis, [12][13][14] the application the block SBL, 24 or the elimination of the interference sound source or the reflection of the impedance plane with the sound field separation, [26][27][28][29][30]34 when combined with the particle velocity measurement in the future.…”

“…13 Combining with the sparse basis functions of CESM, He et al constructs an equivalent redundant dictionary, which can be applied to both spatially sparse and spatially distributed sources. 14 For spatially distributed sources, Hald compared the CESM and its various modified algorithms, and gave the applicability of various algorithms for different types of sound sources. 15 On the other hand, Fernandez-Grande and Daudet proposed a block sparse regularization to solve the adaptive problem of spatially distributed continuous sound sources 16 ; and Bai et al proposed an iterative algorithm to solve the block sparse constraint problem.…”

“…13 Combining with the sparse basis functions of CESM, He et al constructs an equivalent redundant dictionary, which can be applied to both spatially sparse and spatially distributed sources. 14 For spatially distributed sources, Hald compared the CESM and its various modified algorithms, and gave the applicability of various algorithms for different types of sound sources. 15…”

A Planar Acoustic Field Reconstruction Method Based on Fast Wave Superposition Spectrum and Sparse Sampling

“…On the basis of the C-ESM, Hu et al [13] studied the reconstruction of sparse sound field through the sparse basis obtained by singular value decomposition of the transfer matrix; a fast sparse acoustic field reconstruction method was proposed to combine the Bayesian compressed sensing with the sparse basis function in the following study [14]. In addition to the C-ESM, there are many methods combining compressed sensing with equivalent source method, for example, compressed fused model equivalent source method (CFMESM) [15], compressed velocity-mode equivalent source method (CVMESM) [16], and fused total generalized variation (FTGV) [17].…”

“…e particle velocity maps will have sharp peaks in CVMESM [15]. e mode scaling factor was set in CFMESM, and the need for the parameter is a weakness of the method [16].…”