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State estimation is a fundamental function in modern energy management system (EMS), but its results may be vulnerable to false data injection attacks (FDIA). FDIA is able to change the estimation results without being detected by the traditional bad data detection algorithms. In this paper, we propose an accurate and computational attractive approach for FDIA detection. We first rely on the low rank characteristic of the measurement matrix and the sparsity of the attack matrix to reformulate the FDIA detection as a matrix separation problem. Then, four algorithms that solve for this problem are presented and compared, including the traditional Augmented Lagrange Multipliers (ALM), double-noise-dual-problem ALM (DNDP-ALM), the Low Rank Matrix Factorization (LMaFit) and the proposed new "Go Decomposition (GoDec)". Numerical simulation results show that our GoDec outperforms the other three alternatives and demonstrates a much higher computational efficiency. Furthermore, GoDec is shown to be able to handle measurement noise and applicable for large-scale attacks. 