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This paper studies a reference-assisted approach for interference canceling (IC) in microphone array systems. Conventionally, reference-assisted IC is based on the zero crosstalk assumption; i.e., when the desired source signal is absent in the reference microphones. In applications where crosstalk is inevitable, the conventional IC approach usually exhibits degraded performance due to cancellation of the desired signal. In this paper, we develop a crosstalk resilient IC method based on the Capon beamforming technique. The proposed beamformer deals with the uncertainty of crosstalk by applying a constraint on the worst-case crosstalk magnitude. The proposed beamformer not only performs IC, it also provides blind beamforming of the desired signal. We show that a blind beamformer based on the traditional minimum-mean-square-error (MMSE) IC method is a special case of the proposed beamformer. One key step of implementing the proposed Capon beamformer lies in solving a difficult nonconvex optimization problem, and we illustrate how the Capon optimal solution can be effectively approximated using the so-called semidefinite relaxation algorithm. Simulation results demonstrate that the proposed beamformer is more robust against crosstalk-induced signal cancellation than beamformers based on the MMSE-IC methods.