The linear sampling method (LSM) is a very popular method for determining the boundary of an object from the scattered field. However, there are instances where LSM provides the convex hull of the boundary rather than the true boundary. There are two common generalizations to LSM: the Generalized Linear Sampling Method (GLSM) and the Multipoles-based Linear Sampling Method (MLSM). In this paper, the ability of GLSM and MLSM to overcome some of the deficiencies of LSM are investigated. It is found that GLSM may be ideal for imaging thin features of scatterers and that MLSM can provide an improvement over LSM in a more general sense. GLSM may also require user input to adjust the indicator function whereas MLSM does not appear to rely as much on indicator function adjustments for adequate results.
James E. Richie,
"A Comparison of Two Generalizations to the Linear Sampling Method for Inverse Scattering," Progress In Electromagnetics Research M,
Vol. 114, 49-57, 2022. doi:10.2528/PIERM22081807
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