The Lt-norm method is one of the widely used matching filters for adaptive multiple subtraction. When the primaries and multiples are mixed together, the L1-norm method might damage the primaries, leading to poor late...The Lt-norm method is one of the widely used matching filters for adaptive multiple subtraction. When the primaries and multiples are mixed together, the L1-norm method might damage the primaries, leading to poor lateral continuity. In this paper, we propose a constrained L1-norm method for adaptive multiple subtraction by introducing the lateral continuity constraint for the estimated primaries. We measure the lateral continuity using prediction-error filters （PEF）. We illustrate our method with the synthetic Pluto dataset. The results show that the constrained L1-norm method can simultaneously attenuate the multiples and preserve the primaries.展开更多
The lasso of Tibshirani （1996） is a least-squares problem regularized by the l1 norm. Due to the sparseness promoting property of the l1 norm, the lasso has been received much attention in recent years. In this pape...The lasso of Tibshirani （1996） is a least-squares problem regularized by the l1 norm. Due to the sparseness promoting property of the l1 norm, the lasso has been received much attention in recent years. In this paper some basic properties of the lasso and two variants of it are exploited. Moreover, the proximal method and its variants such as the relaxed proximal algorithm and a dual method for solving the lasso by iterative algorithms are presented.展开更多
基金This work is sponsored by National Natural Science Foundation of China （No. 40874056）, Important National Science ＆ Technology Specific Projects 2008ZX05023-005-004, and the NCET Fund.Acknowledgements The authors are grateful to Liu Yang, and Zhu Sheng-wang for their constructive remarks on this manuscript.
文摘The Lt-norm method is one of the widely used matching filters for adaptive multiple subtraction. When the primaries and multiples are mixed together, the L1-norm method might damage the primaries, leading to poor lateral continuity. In this paper, we propose a constrained L1-norm method for adaptive multiple subtraction by introducing the lateral continuity constraint for the estimated primaries. We measure the lateral continuity using prediction-error filters （PEF）. We illustrate our method with the synthetic Pluto dataset. The results show that the constrained L1-norm method can simultaneously attenuate the multiples and preserve the primaries.
文摘The lasso of Tibshirani （1996） is a least-squares problem regularized by the l1 norm. Due to the sparseness promoting property of the l1 norm, the lasso has been received much attention in recent years. In this paper some basic properties of the lasso and two variants of it are exploited. Moreover, the proximal method and its variants such as the relaxed proximal algorithm and a dual method for solving the lasso by iterative algorithms are presented.
