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The regularized sparse recovery (RSR) method proposed for optical power monitoring (OPM) has high performance in practice. However, due to its implementation based on interior point method (IPM), it has high computational complexity for real-time OPM system, especially when the number of monitored channels is large. In this paper, we modify the RSR method and propose an efficient implementation of the modified RSR based on the separable surrogate functions (SSF) technique. The resulting algorithm can be realized by simple hardware structure with low computational complexity. Simulation results confirm that accurate and fast optical power spectrum estimation can be achieved with a low-cost tunable optical filter (TOF) by using the proposed method.