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本文研究了地震数据的稀疏分解问题.提出了一种用高斯束稀疏分解表示地震数据的方法.这是一个拟0范数约束优化问题.在求解拟0范数极小化问题的过程中,通过扫描同相轴的方法实现高斯束稀疏分解,数值实现上提出了使用一种快速单调下降的梯度优化方法.本文提出的稀疏优化方法同时具有去噪的功能,数据模拟试验表明了本方法的可行性和可靠性.
This paper studies the sparse decomposition of seismic data and proposes a method of sparse decomposition of seismic data using Gaussian beam, which is a quasi-zero norm constrained optimization problem.In the process of solving quasi-zero norm minimization problem, Gaussian beam sparse decomposition is achieved by scanning the in-phase method, and a fast and monotonically decreasing gradient optimization method is proposed in the numerical implementation.The sparse optimization method proposed in this paper has the function of denoising at the same time. The data simulation shows that the method is feasible Sexuality and reliability.