论文标题
数据完成的总变异最小化的近似理论
Approximation Theory of Total Variation Minimization for Data Completion
论文作者
论文摘要
总变化（TV）最小化是现代信号/图像处理中最重要的技术之一，并且具有广泛的应用。尽管在压缩感测框架中，最近有许多关于电视最小化的恢复保证的作品，但几乎没有关于恢复部分观察的修复保证的作品。本文是为了分析从随机入口样品中基于电视的恢复的错误。特别是，我们估算了基础原始数据与插值的近似解决方案之间的误差（或根据噪声级别绑定的误差近似），在所有可能的解决方案中具有最小的电视分子仪的给定数据。最后，我们进一步将离散模型的误差估计与稀疏梯度恢复问题以及与基础真实数据来自的基础函数的近似结合在一起。
Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in the framework of compressed sensing, there are few works on the restoration guarantee of the restoration from partial observations. This paper is to analyze the error of TV based restoration from random entrywise samples. In particular, we estimate the error between the underlying original data and the approximate solution that interpolates (or approximates with an error bound depending on the noise level) the given data that has the minimal TV seminorm among all possible solutions. Finally, we further connect the error estimate for the discrete model to the sparse gradient restoration problem and to the approximation to the underlying function from which the underlying true data comes.
