Robust DC optimization and its application in medical image processing

Abstract

BACKGROUND: Many medical image processing problems can be translated into solving the optimization models. In reality, there are lots of nonconvex optimization problems in medical image processing. OBJECTIVE: In this paper, we focus on a special class of robust nonconvex optimization, namely, robust optimization where given the parameters, the objective function can be expressed as the difference of convex functions. METHODS: We present the necessary condition for optimality under general assumptions. To solve this problem, a sequential robust convex optimization algorithm is proposed. RESULTS: We show that the new algorithm is globally convergent to a stationary point of the original problem under the general assumption about the uncertain set. The application of medical image enhancement is conducted and the numerical result shows its efficiency.