Sparse $$\ell _{1}$$ℓ1 regularisation of matrix valued models for acoustic source characterisation
Sparse $$\ell _{1}$$ℓ1 regularisation of matrix valued models for acoustic source characterisation
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DOI：
10.1007/s11081-017-9357-2
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发表时间：
2016-07
影响因子：
2.1
通讯作者：
Laurent Hoeltgen;M. Breuß;G. Herold;E. Sarradj
中科院分区：
文献类型：
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作者：
Laurent Hoeltgen;M. Breuß;G. Herold;E. Sarradj
我们提出了一种策略，在声学工程中的一个常见的问题，这是重建声源的水平和位置应用麦克风阵列测量的稀疏解决方案的恢复。所考虑的任务具有相似的基础追求形式主义，但也依赖于额外的模型假设，从数学的角度来看是具有挑战性的。我们的方法重新制定了原来的任务作为一个凸优化模型。所寻求的解决方案应是具有某种所需结构的矩阵。我们通过额外的约束来加强这种结构。通过结合流行的分裂算法和矩阵微分理论在一个新的框架，我们得到了一个数字有效的战略。除了彻底的理论考虑，我们还提供了一个实验装置，证明我们的策略的可用性。最后，我们还解决了实际问题，如处理不准确的测量和腐败的给定数据。我们提供了一个后处理步骤，能够在这种情况下产生几乎完美的解决方案。
We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears similarities to the basis pursuit formalism but also relies on additional model assumptions that are challenging from a mathematical point of view. Our approach reformulates the original task as a convex optimisation model. The sought solution shall be a matrix with a certain desired structure. We enforce this structure through additional constraints. By combining popular splitting algorithms and matrix differential theory in a novel framework we obtain a numerically efficient strategy. Besides a thorough theoretical consideration we also provide an experimental setup that certifies the usability of our strategy. Finally, we also address practical issues, such as the handling of inaccuracies in the measurement and corruption of the given data. We provide a post processing step that is capable of yielding an almost perfect solution in such circumstances.