A Convex and Exact Approach to Discrete Constrained TV-L1 Image Approximation

作者：Yuan Jing^*; Shi Juan; Tai Xue Cheng

来源：East Asian Journal on Applied Mathematics, 2011, 1(2): 172-186.

DOI：10.4208/eajam.220310.181110a

• Convex optimization
• primal-dual approach
• total-variation regularization
• image processing

We study the TV-L1 image approximation model from primal and dual perspective, based on a proposed equivalent convex formulations. More specifically, we apply a convex TV-L1 based approach to globally solve the discrete constrained optimization problem of image approximation, where the unknown image function u(x) is an element of {f(1), ... ,f(n)}, for all x is an element of Omega. We show that the TV-L1 formulation does provide an exact convex relaxation model to the non-convex optimization problem considered. This result greatly extends recent studies of Chan et al., from the simplest binary constrained case to the general gray-value constrained case, through the proposed rounding scheme. In addition, we construct a fast multiplier-based algorithm based on the proposed primal-dual model, which properly avoids variability of the concerning TV-L1 energy function. Numerical experiments validate the theoretical results and show that the proposed algorithm is reliable and effective.

• 出版日期2011-5
• 单位南阳理工学院