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We propose a fast algorithm to reconstruct a spectrally sparse signal from a small number of randomly observed time domain samples.Different from conventional compressed sensing where frequencies are discretized,we consider the super-resolution case where the frequencies can be any values in the normalized continuous frequency domain [0,1).Our signal recovery problem can be converted into a low rank Hankel matrix completion problem,for which we propose an efficient feasible point algorithm named projected gradient algorithm(PGA).We give the convergence analysis of the algorithm.The algorithm can be further accelerated by the FISTA-like technique.Numerical experiments are provided to illustrate the effectiveness of our proposed algorithm.