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.

翻译：全面变异(TV)最小化是现代信号/图像处理中最重要的技术之一,具有广泛的应用范围。虽然最近有许多关于在压缩遥感框架内恢复电视最小化保障的工程,但从局部观测中恢复恢复电视最小化的工程寥寥无几。本文旨在分析从随机入境样本中恢复电视的错误。特别是,我们估计了原始原始原始数据和(或根据噪音程度与差错相近)在各种可能的解决办法中具有最低电视半调的给定数据之间的大致解决办法之间的错误。最后,我们进一步将离散模型的误差估计与稀有梯度恢复问题和基本真实数据产生的基本功能的近似值联系起来。