Fast acoustic source imaging using multi-frequency sparse data

We consider the acoustic source imaging problems using multiple frequency data. Using the data of one observation direction/point, we prove that some information (size and location) of the source support can be recovered. A non-iterative method is then proposed to image the source for the Helmholtz equation using multiple frequency far field data of one or several observation directions. The method is simple to implement and extremely fast since it only computes an indicator function on the interested domain using only matrix vector multiplications. Numerical examples are presented to validate the effectiveness of the method.

[1]  Yukun Guo,et al.  Fourier method for recovering acoustic sources from multi-frequency far-field data , 2017 .

[2]  Xiaodong Liu,et al.  A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency , 2017, 1701.00537.

[3]  Jiguang Sun,et al.  Efficient finite element method for grating profile reconstruction , 2015, J. Comput. Phys..

[4]  William Rundell,et al.  A Recursive Algorithm for MultiFrequency Acoustic Inverse Source Problems , 2015, SIAM J. Numer. Anal..

[5]  A. E. Badia,et al.  An Inverse Source Problem in Potential Analysis , 2000 .

[6]  A. Devaney,et al.  Nonuniqueness in inverse source and scattering problems , 1982 .

[7]  Nicolas Valdivia,et al.  Acoustic source identification using multiple frequency information , 2009 .

[8]  Roland Griesmaier,et al.  A Factorization Method for Multifrequency Inverse Source Problems with Sparse Far Field Measurements , 2017, SIAM J. Imaging Sci..

[9]  Xiaodong Liu,et al.  Reconstruction of Neumann eigenvalues and support of sound hard obstacles , 2014 .

[10]  Per Christian Hansen,et al.  Sound source reconstruction using inverse boundary element calculations. , 2003, The Journal of the Acoustical Society of America.

[11]  Anthony J. Devaney,et al.  Inverse Source Problem in Nonhomogeneous Background Media , 2007, SIAM J. Appl. Math..

[12]  Junshan Lin,et al.  A multi-frequency inverse source problem , 2010 .

[13]  Roland Potthast,et al.  A study on orthogonality sampling , 2010 .

[14]  George Dassios,et al.  Electric and Magnetic Activity of the Brain in Spherical and Ellipsoidal Geometry , 2009 .

[15]  Jiguang Sun,et al.  An eigenvalue method using multiple frequency data for inverse scattering problems , 2012 .

[16]  Roland Griesmaier,et al.  Multi-frequency orthogonality sampling for inverse obstacle scattering problems , 2011 .

[17]  T. Ha-Duong,et al.  On an inverse source problem for the heat equation. Application to a pollution detection problem , 2002 .

[18]  Xia Ji,et al.  Direct sampling methods for inverse elastic scattering problems , 2017, 1711.00626.

[19]  Igor Malyshev,et al.  An inverse source problem for heat equation , 1989 .

[20]  John Sylvester,et al.  A scattering support for broadband sparse far field measurements , 2005 .