Hongxia Guo

Guanqiu Ma, Hongxia Guo, Guanghui Hu

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we establish a computational criterion that characterizes both the unknown pulse moments and the narrowest strip (perpendicular to the direction) enclosing the source support. Central to our inversion scheme is the construction of indicator functions, defined pointwise over the spatial and temporal sampling variables. The proposed inversion scheme permits the recovery of the $Θ$-convex support domain from far-field data at sparse observation directions. Uniqueness in determining the convex hull of the support and the excitation instants-using all observation directions-is also established as a direct consequence of the factorization method. The effectiveness and feasibility of the approach are examined through comprehensive numerical simulations in two and three dimensions.

Hao Gu, Hongxia Guo, Xiang Xu et al.

In this paper, we develop a novel multi-frequency factorization method to reconstruct the spatial support of the ambient noise source. The proposed method only requires sparse correlation data and has low computational cost. Numerical experiments in two and three dimensions are presented to demonstrate the effectiveness of the proposed method.