Extraction of target sources from incoherent and partially coherent background noise using low-rank and sparse decomposition of the cross-spectral matrix

Beamforming in acoustic measurements suffers from strong and complicated background noise, which is usually assumed to be incoherent and contributes to the diagonal part of the cross-spectral matrix (CSM). However,n in some measurements the background noise could frequently be partially coherent and contributes to the off-diagonal part of the matrix as well. The complicated background noise would also lead to uninterpretable beamforming results, especially in aeroacoustic measurements. A method was proposed in this study to extract the target sources from incoherent and partially coherent background noise in acoustic measurements. Different characteristics between the target sources and background noise were analyzed. The sources and noise were modeled as low-rank and weak sparsity, and separated by minimization of a rank and L0-norm function. The number of eigenvalues was reduced in the extracted source containment of CSM. The eigenvalue and related beamforming results showed that the method was robustness in the extraction of target sources from complicated background noise.