Randomized Projection Methods for Linear Systems with Arbitrarily Large Sparse Corruptions
Randomized Projection Methods for Linear Systems with Arbitrarily Large Sparse Corruptions
复制标题
具有任意大稀疏损坏的线性系统的随机投影方法
DOI：
10.1137/18m1179213
复制
发表时间：
2019
影响因子：
3.1
通讯作者：
Needell, Deanna
中科院分区：
文献类型：
--
作者：
Haddock, Jamie;Needell, Deanna
在医学成像、纠错和传感器网络等应用中，需要解决可能被少量任意大的破坏破坏的大规模线性系统。我们考虑解决这样的大型系统的线性方程是不一致的，由于腐败的测量矢量。以此作为我们激励的例子，我们开发了一种方法，这种设置，允许检测损坏的条目，从而收敛到原始系统的“真正”的解决方案。我们为我们的方法提供了分析依据，并在真实的和合成系统上提供了实验证据。
In applications like medical imaging, error correction, and sensor networks, one needs to solve large-scale linear systems that may be corrupted by a small number of arbitrarily large corruptions. We consider solving such large-scale systems of linear equationsthat are inconsistent due to corruptions in the measurement vector. With this as our motivating example, we develop an approach for this setting that allows detection of the corrupted entries and thus convergence to the “true” solution of the original system. We provide analytical justification for our approaches as well as experimental evidence on real and synthetic systems.