A novel convex optimization problem formulation for source localization using partly calibrated arrays composed of subarrays with unknown displacements is introduced. The proposed formulation is based on sparse reconstruction using a mixed trace- and ℓ₁-norm minimization and exploits joint sparsity and special structure in the signal model. The new technique is applicable to subarrays of arbitrary topologies and allows the joint estimation of the directions of arrival (DoAs) and the array calibration. As shown by simulations, our new DoA estimation technique outperforms the state of the art method RARE, especially in low number of snapshot and low signal-to-noise ratio regime.