Sparse $$\ell _{1}$$ ℓ 1 regularisation of matrix valued models for acoustic source characterisation

Abstract

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.

Announcement: Howard Rosenbrock Prize 2020

“…Previous winners of the award were Jason E. Hicken in 2014 (Hicken 2014), Moritz Simon and Michael Ulbrich in 2015 (Simon and Ulbrich 2015), Taedong Kim and Stephen J. Wright in 2016 (Kim and Wright 2016), Hoai An Le Thi and Tao Pham Dinh and 2017 (Thi and Dinh 2017), Laurent Hoeltgen, Michael Breuß, Gert Herold, and Ennes Sarrad in 2018 (Hoeltgen et al 2018), and Robert Burlacu, Herbert Egger, Martin Groß, Alexander Martin, Marc E. Pfetsch, Lars Schewe, Mathias Sirvent, and Martin Skutella in 2019 (Burlacu et al 2019).…”

Announcement: Howard Rosenbrock Prize 2021

“…Hoai An Le Thi and Tao Pham Dinh (Thi and Dinh 2017), 5. Laurent Hoeltgen, Michael Breuß, Gert Herold, and Ennes Sarrad (Hoeltgen et al 2018), 6. Robert Burlacu, Herbert Egger, Martin Groß, Alexander Martin, Marc E. Pfetsch, Lars Mathias Sirvent, and Martin Skutella (Burlacu et al 2019), and 7.…”