Xufang Li1,2, Zhong Wu1, Fang Zhang1, Deqiang Qu1. 1. Business School, University of Shanghai for Science and Technology, Shanghai, China. 2. Management School, Shanghai University of Engineering Science, Shanghai, China.
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.
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.
Keywords:
Medical image processing; medical image enhancement; robust nonconvex optimization; sequential robust convex optimization algorithm