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Randomized Projection Methods for Linear Systems with Arbitrarily Large Sparse Corruptions
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 equations that 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