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Blended acquisition improves the efficiency of seismic acquisition significantly, but blending noise brings new challenges to subsequent conventional seismic data processing. The efficiency of conventional SSA for rank-reduction using TSVD is low, and its deblending accuracy is open to be improved. Thus, we propose a damped randomized SSA (DRSSA) algorithm using damped randomized SVD (DR-SVD) which combines the high efficiency of R-SVD and the high accuracy of the damping constraint. In addition, a projected gradient descent (PGD) algorithm is introduced for joint deblending and reconstruction of incomplete blended data. The effectiveness and superiority of the proposed method are verified by synthetic data and field marine data examples in improving the deblending efficiency and accuracy.