全变差最小化的样本复杂性
Sample Complexity of Total Variation Minimization
摘要：
这项工作考虑使用总变差（TV）最小化在恢复一个给定的梯度稀疏向量从高斯线性测量。最近的研究表明，在渐近区域TV极小化存在一个尖锐的相变行为。相变曲线指定了大量测量的TV最小化的成功和失败的边界。这是一个具有挑战性的任务，以获得一个理论界，反映这条曲线。在这项工作中，我们提出了一个新的上限，适当地逼近这条曲线，是渐近尖锐的。数值结果表明，我们的界限是更接近经验的电视相变曲线比以前已知的界限得到的Kabanava。
英文摘要：
This work considers the use of Total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exist a sharp phase transition behavior in TV minimization in asymptotic regimes. The phase transition curve specifies the boundary of success and failure of TV minimization for large number of measurements. It is a challenging task to obtain a theoretical bound that reflects this curve. In this work, we present a novel upper-bound that suitably approximates this curve and is asymptotically sharp. Numerical results show that our bound is closer to the empirical TV phase transition curve than the previously known bound obtained by Kabanava.
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