论文标题
与总变异有关的凸问题的一般分解方法
A General Decomposition Method for a Convex Problem Related to Total Variation Minimization
论文作者
论文摘要
我们考虑了在多个图像处理任务中应用的一般总变量最小化问题的双重问题的顺序和并行分解方法，例如图像插入，估计光流以及缺失小波系数的重建。在希尔伯特空间设置中分析了这些方法与全局问题解决方案的收敛性，并提供了收敛速度。因此，这些融合结果不仅适用于精确的局部最小化，而且还可以大约解决子问题。作为近似局部溶液过程的具体示例，提出和分析了替代技术。此外，将获得的收敛率与文献中的相关结果进行了比较，并证明与它们一致甚至是对它们一致的。提出了数值实验，以支持理论发现，并显示图像插入，光流估计和波浪插入任务中所提出的分解算法的性能。
We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and reconstruction of missing wavelet coefficients. The convergence of these methods to a solution of the global problem is analysed in a Hilbert space setting and a convergence rate is provided. Thereby, these convergence result hold not only for exact local minimization but also if the subproblems are just solved approximately. As a concrete example of an approximate local solution process a surrogate technique is presented and analysed. Further, the obtained convergence rate is compared with related results in the literature and shown to be in agreement with or even improve upon them. Numerical experiments are presented to support the theoretical findings and to show the performance of the proposed decomposition algorithms in image inpainting, optical flow estimation and wavelet inpainting tasks.
