Acoustical source reconstruction from non-synchronous sequential measurements by Fast Iterative Shrinkage Thresholding Algorithm. (10th November 2017) - Yu, Liang; Antoni, Jerome; Leclere, Quentin; Jiang, Weikang
Abstract: Acoustical source reconstruction is a typical inverse problem, whose minimum frequency of reconstruction hinges on the size of the array and maximum frequency depends on the spacing distance between the microphones. For the sake of enlarging the frequency of reconstruction and reducing the cost of an acquisition system, Cyclic Projection (CP), a method of sequential measurements without reference, was recently investigated (JSV, 2016, 372:31-49). In this paper, the Propagation based Fast Iterative Shrinkage Thresholding Algorithm (Propagation-FISTA) is introduced, which improves CP in two aspects: (1) the number of acoustic sources is no longer needed and the only making assumption is that of a "weakly sparse" eigenvalue spectrum; (2) the construction of the spatial basis is much easier and adaptive to practical scenarios of acoustical measurements benefiting from the introduction of propagation based spatial basis. The proposed Propagation-FISTA is first investigated with different simulations and experimental setups and is next illustrated with an industrial case. Abstract : Highlights: Sequential measurements without reference is investigated by formulating it as spectral matrix completion problem. Propagation-FISTA is proposed based on weakly sparse assumption of eigenvalue spectrum. The proposed method is validated both in laboratorial and industrial setups.