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摘要: 提出了一种保持边缘的正则化图像恢复算法,该方法可有效地用于求解线性逆问题的 非凸优化过程.通过对正则化函数及相应泛函性质的理论分析,得出了使泛函达到最小的正则 化函数表达式;引入一个与原非凸泛函相应的二元泛函,将非凸优化问题转化为本质上的凸优 化问题,采用松弛迭代算法获得非凸优化问题的局部极小解;证明了所提出的算法是全局收敛 的.通过实验验证了算法的有效性.Abstract: A new algorithm for edge-preserving image restoration is presented in this paper. The variation based method can be effectively used in the process of non-con vex optimization for solving the linear inverse problem. By analyzing the properties of regularization functions and the corresponding energy functional, an optimal expression of regularization function and a new energy functional with binary variables are in troduced. Thus the non-convex optimization problem is transformed into a sequence of essentially convex one. The local optimal solution of non convex optimization problem is then obtained by using a relaxation iterative algorithm. Such algorithm is shown to be globally convergent. Finally, the proposed method is tested on real and synthetic images.
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Key words:
- Regularization /
- image restoration /
- variation /
- global convergence
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