A modified total variation approach for single frequency inverse scattering

The Linear Sampling Method (LSM) is a relatively novel method of solving the inverse acoustic or electromagnetic scattering problem. The linear formulation of the inverse problem, which is due to an exact linear relationship that is satisfied by far-field data, makes LSM imaging in the presence of multiple scattering a straightforward linear algebra procedure. The main drawback of the LSM is its dependence on copious data. In this work we seek to improve LSM reconstruction performance by considering undersampled single frequency multi-static far-field data coupled with a spatial gradient constraint on the regularized image. The resulting total-variation-type optimization problem is then solved by means of an alternating minimization scheme.