TY - GEN A1 - Hoeltgen, Laurent A1 - Breuß, Michael A1 - Herold, Gert A1 - Sarradj, Ennes T1 - Sparse ℓ1 regularisation of matrix valued models for acoustic source characterisation T2 - Optimization and Engineering N2 - 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. KW - Convex optimisation KW - Sparse recovery KW - Split Bregman KW - Microphone array KW - Matrix differentiation KW - Acoustic source characterisation Y1 - 2018 UR - https://opus4.kobv.de/opus4-UBICO/frontdoor/index/index/docId/21554 SN - 1389-4420 SN - 1573-2924 VL - 19 IS - 1 SP - 39 EP - 70 ER -