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We propose an approximation framework for distributed target localization in sensor networks. We represent the unknown target positions on a location grid as a sparse vector, whose support encodes the multiple target locations. The location vector is linearly related to multiple sensor measurements through a sensing matrix, which can be locally estimated at each sensor. We show that we can successfully determine multiple target locations by using linear dimensionality-reducing projections of sensor measurements. The overall communication bandwidth requirement per sensor is logarithmic in the number of grid points and linear in the number of targets, ameliorating the communication requirements. Simulations results demonstrate the performance of the proposed framework.