Retrieval of acoustic sources from multi-frequency phaseless data

Abstract

This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a major challenge associated with such an inverse problem. We develop a novel strategy to overcome this challenging problem by recovering the radiated fields via adding some reference point sources as extra artificial sources to the inverse source system. This novel reference source technique requires only a few extra data, and brings in a simple phase retrieval formula. The stability of this phase retrieval approach is rigorously analyzed. After the reacquisition of the phase information, the multi-frequency inverse source problem with recovered phase information is solved by the Fourier method, which is non-iterative, fast and easy to implement. Several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.

arXiv comment27 pages, 4 figures

References in corpus (11)

• Determining both sound speed and internal source in thermo- and photo-acoustic tomography
• Recovering scattering obstacles by multi-frequency phaseless far-field data
• Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensions
• Imaging of locally rough surfaces from intensity-only far-field or near-field data
• Uniqueness of a 3-D coefficient inverse scattering problem without the phase information
• Stability estimates for linearized near-field phase retrieval in X-ray phase contrast imaging
• Fast acoustic source imaging using multi-frequency sparse data
• On an inverse boundary problem arising in brain imaging
• A reference ball based iterative algorithm for imaging acoustic obstacle from phaseless far-field data
• Fourier method for identifying electromagnetic sources with multi-frequency far-field data
• Locating multiple multipolar acoustic sources using the direct sampling method

Cited by in corpus (12)

• Determining a random Schrödinger operator: both potential and source are random
• A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data
• A convergent numerical method for a multi-frequency inverse source problem in inhomogenous media
• An inverse acoustic-elastic interaction problem with phased or phaseless far-field data
• Uniqueness in inverse cavity scattering problems with phaseless near-field data
• Modified Tikhonov regularization for identifying several sources
• A reference ball based iterative algorithm for imaging acoustic obstacle from phaseless far-field data
• Uniqueness in inverse acoustic scattering with phaseless near-field measurements
• Recovering the initial condition of parabolic equations from lateral Cauchy data via the quasi-reversibility method
• Inverse electromagnetic source scattering problems with multi-frequency sparse phased and phaseless far field data
• Machine learning based data retrieval for inverse scattering problems with incomplete data
• An approximate factorization method for inverse acoustic scattering with phaseless total-field data