Does Compressed Sensing have applications in Robust Statistics? by Salvador Flores
The connections between robust linear regression and sparse reconstruction are brought to light. We show that in the context of xed design, the notion of breakdown point coincides with exact recovery of sparse signals from highly incomplete information. The main consequence of this connection in robust regression is that there exists, for any dimension, \many" designs on which the l_1 estimator has a positive breakdown point. This result clarifies a common misunderstanding on the robustness of M-estimators.
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