Reconstruction of acoustic sources from multi-frequency phaseless far-field data

2020/02/09 by Zhang, Deyue, Guo, Yukun, Sun, Fenglin +1
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2002.03279

Abstract

We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering the phase information of far-field data. This reference source technique leads to an easy-to-implement phase retrieval formula. Mathematically, the stability of the phase retrieval approach is rigorously justified. Then we employ the Fourier method to deal with the multi-frequency inverse source problem with recovered phase information. Finally, some two and three dimensional numerical results are presented to demonstrate the viability and effectiveness of the proposed method.

Related

• Identifying an acoustic source in a two-layered medium from multi-frequency phased or phaseless far-field patterns
• Inverse source problem of the biharmonic equation from multi-frequency phaseless data
• Phaseless inverse source scattering problem: phase retrieval, uniqueness and direct sampling methods
• Uncertainty principles for inverse source problems, far field splitting and data completion
• Inverse electromagnetic source scattering problems with multi-frequency sparse phased and phaseless far field data