Subspace-based Optimization Method with Adaptive Total Variation for Microwave Imaging

Microwave imaging problems are nonlinear and ill-posed due to multiple scattering and a lack of observed data. The optimization method with total variation (TV) regularization can be used to address the ill-posed problems. However, TV regularization is susceptible to the staircase effect, which blurs the edges. In order to alleviate the staircase effect, in this study, the
$\boldsymbol{\mathrm{L}^{\mathrm{p}}}$
-norm TV as the regularization factor is applied to the subspace-based optimization method, and parameter p is adaptively adjusted to the gradient of the image. It can not only avoid the staircase effect but also eliminate noise in measured scattering data. Numerical experiments prove that the method not only has good reliability but also preserves the local feature of the object.