We solve a decentralized basis pursuit problem in a multiagent system, where each agent holds part of the linear observations on a common sparse vector, and all the agents collaborate to recover the sparse vector through limited neighbor-to-neighbor communication. The proposed decentralized linearized Bregman algorithm solves the Lagrange dual of an augmented l1 model that is equivalent to basis pursuit. The fact that this dual problem is unconstrained and differentiable enables a lightweight yet efficient decentralized gradient algorithm. We prove nearly linear convergence of the algorithm in the sense that uniformly for every agent i, the error obeys |x_i(k) - x*|<=e(k) and e(k)<=rho e(k-1)+gamma, where rho<=1 and gamma>=0 are independent of k or i. Numerical experiments demonstrate this convergence.