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We consider the problem of estimating a signal subspace in the presence ofinterference that contaminates some proportion of the received observations.Our emphasis is on detecting the contaminated observations so that the signalsubspace can be estimated with the contaminated observations discarded. To thisend, we employ a signal model which explicitly includes an interference termthat is distinct from environmental noise. To detect when the interference termis nonzero, we estimate the interference term using an optimization problemwith a sparsity-inducing group SLOPE penalty which accounts for simultaneoussparsity across all channels of the multichannel signal. We propose aniterative algorithm which efficiently computes the observations estimated tocontain interference. Theoretical support for the accuracy of our interferenceestimator is provided by bounding its false discovery rate, the expectedproportion of uncontaminated observations among those estimated to becontaminated. Finally, we demonstrate the empirical performance of ourcontributions in a number of simulated experiments.

Signal Subspace Methods Which Are Robust to Impulsive Noise