Inverse Scattering Using a Joint $L1-L2$ Norm-Based Regularization

Inverse scattering problems suffer from ill-posedness and ill-conditioning, necessitating the use of regularization methods to get meaningful solutions. Commonly used regularizations are L2 norm based, but these generate over-smooth solutions. We propose a regularization method using both the L1 and L2 norms to obtain sharp object boundaries, while also achieving good interior reconstruction of the object permittivity. Knowledge about the permittivity can also be used as a priori information. The applicability of the method is demonstrated on synthetically generated data for two-dimensional (2-D) microwave imaging using the Born-iterative method (BIM). The optimization routine systematically estimates all parameters, while minimizing the cost function. Different objects chosen to represent realistic features have been considered to evaluate the performance. The reconstructed images indicate that the method can produce accurate object localization, shape identification, and good permittivity estimation.