Measurement data in linear systems arising from real-world applications often suffers from both large, sparse corruptions, and widespread small-scale noise. This can render many popular solvers ineffective, as the least squares solution is far from the desired solution, and the underlying consistent system becomes harder to identify and solve. QuantileRK is a member of the Kaczmarz family of iterative projective methods that has been shown to converge exponentially for systems with arbitrarily large sparse corruptions. In this paper, we extend the analysis to the case where there are not only corruptions present, but also noise that may affect every data point, and prove that QuantileRK converges with the same rate up to an error threshold. We give both theoretical and experimental results demonstrating QuantileRK's strength.

翻译：现实世界应用产生的线性系统中的测量数据往往既存在大量零星的腐败,也存在广泛的小规模噪音。 这使得许多流行的解决方案无效,因为最小的平方解决方案远未达到理想的解决方案,基础一致的系统也更加难以识别和解决。 Quantilerk是Kaczmarz家族的迭代投影方法的成员,这些方法被证明是任意的大规模腐败系统指数化的。 在本文中,我们将分析扩大到不仅存在腐败而且噪音可能影响每个数据点的情况,并证明Qautilerk与同一速度相融合,达到一个错误门槛。 我们给出理论和实验结果来证明Qatilerk的强度。