图像恢复中的非凸非光滑变分模型及其数值算法研究

项目名称： 图像恢复中的非凸非光滑变分模型及其数值算法研究

项目编号： No.61201455

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 殷海青

作者单位： 中国石油大学（华东）

项目金额： 27万元

中文摘要： 非凸非光滑的变分正则模型能很好地刻画具有光滑轮廓和清晰边缘的图像，较其它变分模型在图像复原和重建时优越，逐渐成为信号和图像处理领域中最受欢迎的技术之一。但对于这一问题，现有的算法不能满足大规模数据处理的需要，如何构建好的模型和设计高效的数值算法是一个非常有意义的研究课题。本项目结合最优化理论和变分正则化的最新进展，拟对如下问题展开研究：(1)通过引入光滑化因子及光滑化方法，充分利用梯度信息克服不可微的缺点；(2)将问题转化为约束非线性方程组或非线性互补问题来改进其收敛速度及收敛性理论；(3)对于非负图像恢复往往对应着界约束的非线性规划，利用梯度型或原对偶内点型算法并结合积极集的策略，提出高效算法。本项目立足模型选择的理论依据和设计具有全局收敛性的算法，具有一定的开创性和前沿性，研究成果相信会推动图像恢复的应用和发展。

中文关键词： 图像恢复；非凸非光滑正则化；非线性规划；；

英文摘要： Nonconvex nonsmooth regularization has advantages over convex regularization for image restoration. Nonsmooth nonconvex regularization offers a restored image composing of constant regions surrounded by closed contours and neat edges.So this method become one of the popular techniques. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization.In this project, based on optimization theory and variational regularization, smoothing factor and smoothing method can solve the nondifferential objective function effectively. Then the problem will be translated into constrained nonlinear equations or nonlinear complementary problem using two order derivative for improving the calculation speed. At the same time. we also give theoretical analysis about the convergence. On the other hand, image restoration with nonnegative constraints will lead to nonlinear programming with bound constraints. By gradient type method for optimization and active set, fast numerical algorithm is proposed. so this project mainly proposes the nonconvex nonsmooth variational model and gives some global convergence algorithms. It will accelerate rhe development for image restoration.

英文关键词： image restoration nonconvex nonsmooth regularizati；nonlinear programming；；；