论文标题
用于截短的二次正则化的凸算法的预处理差异，并应用于成像
A Preconditioned Difference of Convex Algorithm for Truncated Quadratic Regularization with Application to Imaging
论文作者
论文摘要
我们考虑使用梯度运算符的截断二次正则化的最小化问题，这是一个非滑动和非凸问题。我们将线性方程式的经典预处理配合到具有外推的凸函数算法的非线性差异。特别是，我们的预处理框架可以有效地处理大型线性系统，这通常对于计算而言是昂贵的。保证全局收敛，并根据对最小化功能的Kurdyka-lojasiewicz指数的分析给出了局部线性收敛速率。提出的带有预处理的算法证明对图像恢复非常有效，并且对图像分割也有吸引力。
We consider the minimization problem with the truncated quadratic regularization with gradient operator, which is a nonsmooth and nonconvex problem. We cooperated the classical preconditioned iterations for linear equations into the nonlinear difference of convex functions algorithms with extrapolation. Especially, our preconditioned framework can deal with the large linear system efficiently which is usually expensive for computations. Global convergence is guaranteed and local linear convergence rate is given based on the analysis of the Kurdyka-Łojasiewicz exponent of the minimization functional. The proposed algorithm with preconditioners turns out to be very efficient for image restoration and is also appealing for image segmentation.
