Can one trade sensor quality for quantity? While larger networks with greater sensor density promise to allow us to use noisier sensors yet measure subtler phenomena, aggregating data and designing decision rules is challenging. Motivated by dense, participatory seismic networks, we seek efficient aggregation methods for event detection. We propose to perform aggregation by sparsification: roughly, a sparsifying basis is a linear transformation that aggregates measurements from groups of sensors that tend to co-activate, and each event is observed by only a few groups of sensors. We show how a simple class of sparsifying bases provably improves detection with noisy binary sensors, even when only qualitative information about the network is available. We then describe how detection can be further improved by learning a better sparsifying basis from network observations or simulations. Learning can be done offline, and makes use of powerful off-the-shelf optimization packages. Our approach outperforms state of the art detectors on real measurements from seismic networks with hundreds of sensors, and on simulated epidemics in the Gnutella P2P communication network.