Yardibi Tarik, Li Jian, Stoica Petre, Cattafesta Louis N
Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida 32611, USA.
J Acoust Soc Am. 2008 May;123(5):2631-42. doi: 10.1121/1.2896754.
Using microphone arrays for estimating source locations and strengths has become common practice in aeroacoustic applications. The classical delay-and-sum approach suffers from low resolution and high sidelobes and the resulting beamforming maps are difficult to interpret. The deconvolution approach for the mapping of acoustic sources (DAMAS) deconvolution algorithm recovers the actual source levels from the contaminated delay-and-sum results by defining an inverse problem that can be represented as a linear system of equations. In this paper, the deconvolution problem is carried onto the sparse signal representation area and a sparsity constrained deconvolution approach (SC-DAMAS) is presented for solving the DAMAS inverse problem. A sparsity preserving covariance matrix fitting approach (CMF) is also presented to overcome the drawbacks of the DAMAS inverse problem. The proposed algorithms are convex optimization problems. Our simulations show that CMF and SC-DAMAS outperform DAMAS and as the noise in the measurements increases, CMF works better than both DAMAS and SC-DAMAS. It is observed that the proposed algorithms converge faster than DAMAS. A modification to SC-DAMAS is also provided which makes it significantly faster than DAMAS and CMF. For the correlated source case, the CMF-C algorithm is proposed and compared with DAMAS-C. Improvements in performance are obtained similar to the uncorrelated case.
在航空声学应用中，使用麦克风阵列来估计声源位置和强度已成为常见做法。经典的延迟求和方法存在分辨率低和旁瓣高的问题，由此产生的波束形成图难以解释。声源映射反卷积方法（DAMAS）反卷积算法通过定义一个可表示为线性方程组的逆问题，从受污染的延迟求和结果中恢复实际声源水平。本文将反卷积问题引入稀疏信号表示领域，提出了一种稀疏约束反卷积方法（SC-DAMAS）来解决DAMAS逆问题。还提出了一种稀疏保持协方差矩阵拟合方法（CMF）来克服DAMAS逆问题的缺点。所提出的算法是凸优化问题。我们的模拟表明，CMF和SC-DAMAS的性能优于DAMAS，并且随着测量中噪声的增加，CMF的性能优于DAMAS和SC-DAMAS。据观察，所提出的算法比DAMAS收敛更快。还对SC-DAMAS进行了改进，使其比DAMAS和CMF快得多。对于相关声源情况，提出了CMF-C算法并与DAMAS-C进行比较。与不相关情况类似，性能得到了改善。
