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Network component analysis (NCA) has been established as a promising tool for reconstructing gene regulatory networks from microarray data. NCA is a method that can resolve the problem of blind source separation when the mixing matrix instead has a known sparse structure despite the correlation among the source signals. The original NCA algorithm relies on alternating least squares (ALS) and suffers from local convergence as well as slow convergence. In this paper, we develop new and more robust NCA algorithms by incorporating additional signal constraints. In particular, we introduce the biologically sound constraints that all nonzero entries in the connectivity network are positive. Our new approach formulates a convex optimization problem which can be solved efficiently and effectively by fast convex programming algorithms. We verify the effectiveness and robustness of our new approach using simulations and gene regulatory network reconstruction from experimental yeast cell cycle microarray data.