Novel implementation of the extended sampling method for inverse biharmonic scattering
For researchers in inverse scattering, this work provides a novel ESM that can recover both location and size of obstacles from limited incident waves, but the results are only demonstrated on synthetic data without comparison to existing methods.
This paper develops a new extended sampling method (ESM) for recovering an unknown clamped obstacle in two dimensions from far-field measurements for the biharmonic wave equation. Numerical experiments with synthetic data demonstrate the method's effectiveness with noisy data and show the influence of the reference disk radius on reconstruction.
This paper considers an inverse shape problem for recovering an unknown clamped obstacle in two dimensions from far--field measurements generated by a single incident wave or just a few incident waves for the biharmonic (flexural) wave equation. Here we will develop a new extended sampling method (ESM) that is derived using the analysis of the well--known factorization method. We will also consider an ESM using both sound--soft and sound--hard sampling disks to identify sampling points where the reference disk intersects the unknown cavity. The use of a sound--hard sampling disk has not been studied in the literature whereas the sound--soft sampling disk has been used in most recent works. Traditionally the ESM seeks to find the location of the scatterer from limited incident directional data. Here, our method acts more like the factorization method to obtain the location as well as the size (and possibly the shape) of the obstacle. We present numerical experiments with synthetic data that demonstrate how effective this new implementation is with respect to noisy data and illustrate the influence of the reference disk radius on the reconstruction.