中文摘要：

利用高分辨率稀疏Radon变换和正交变换两种原子构成过完备的信号重构空间,使得地震信号在此高阶高分辨率稀疏Radon变换域中能够被稀疏表示;结合基于过完备字典的信号稀疏表示,提出高分辨率稀疏Radon变换和正交多项式变换结合的高阶稀疏Radon变换（HOSRT）。所提方法通过将地震数据和预测多次波变换到高阶稀疏Radon空间,用完备的高阶稀疏Radon变换原子稀疏表示,并在该域进行自适应相减,能够有效分离一次波和多次波;而且由于构造的完备空间克服了正交性的问题,压制过程中降低了对一次波的损伤。对合成地震记录和实际资料的处理结果表明该方法能够提高多次波的压制效果,同时还可以较好地保留一次波振幅AVO（振幅随偏移别距的变化）特性。

英文摘要：

An adaptive subtraction in high-order sparse Radon domain for multiple-elimination is proposed. Subtraction in time domain can damage primary while it is overlapped with multiples. Radon transform is not an orthogonal transformation; its inversion will loss data trivial. For primary-preservation,the high-resolution sparse Radon transform is incorporated with orthogonal polynomial transformation and sparse representation by an overcomplete dictionary,thus a high-order sparse Radon transform is achieved. The high-order sparse Radon transform not only keeps primary amplitude but improves the resolution of multiple elimination. The adaptive subtraction in high-order sparse Radon domain will decrease the damage to the primaries. The experiments with synthetic data and field data show good performances in multiple elimination and AVO（ amplitude versus offset）-preservation.