Intensity-only inverse scattering with MUSIC

We present a method for inverse scattering that relies on intensity-only measurements of the scattered field on a single measurement plane. By collecting measurements from a suite of experiments in which the sample is illuminated using different incident fields, we create sufficient data diversity to overcome the limitations of the intensity-only measurements. We give an explicit procedure that uses an algebraic relation called the polarization identity to convert intensity measurements of scattered fields to interferometric measurements in which one of the scattered fields serves as the reference. By adjusting the multiple signal classification (MUSIC) method for these interferometric data, we effectively recover the location and shapes of multiple objects contained in the imaging region. This method is effective and robust to noise as long as there is sufficiently high data diversity and the fractional volume of the scattering objects is not too high. We present image reconstructions for several three-dimensional examples with simulated data computed using the Method of Fundamental Solutions that demonstrate the effectiveness of this imaging method.