Stable Image Reconstruction Using Total Variation Minimization
Stable Image Reconstruction Using Total Variation Minimization
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DOI：
10.1137/120868281
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发表时间：
2013-01-01
影响因子：
2.1
通讯作者：
Ward, Rachel
中科院分区：
文献类型：
--
作者：
Needell, Deanna;Ward, Rachel
本文提出了使用总变差最小化从欠采样噪声测量中恢复稳定且鲁棒的图像的近乎最佳保证。特别是，我们表明，从 O(s log(N)) 非自适应线性测量中，图像可以在其梯度的最佳 s 项近似内重建到对数因子，并且可以通过稍微多一些测量来消除该因子。在此过程中，我们证明了位于适当不相干矩阵的零空间中的函数的强化索博列夫不等式。
This paper presents near-optimal guarantees for stable and robust image recovery from undersampled noisy measurements using total variation minimization. In particular, we show that from O(s log(N)) nonadaptive linear measurements, an image can be reconstructed to within the best s-term approximation of its gradient up to a logarithmic factor, and this factor can be removed by taking slightly more measurements. Along the way, we prove a strengthened Sobolev inequality for functions lying in the null space of a suitably incoherent matrix.