基于自适应压缩感知的地震信号稀疏表示与高效重构

项目名称： 基于自适应压缩感知的地震信号稀疏表示与高效重构

项目编号： No.61202051

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 计算机科学学科

项目作者： 向秀桥

作者单位： 中国地质大学（武汉）

项目金额： 24万元

中文摘要： 受复杂条件限制得到的不完整地震勘探信号常常影响后续的处理解释和最终的油气判断，传统的重建方法受香农采样定理的约束来采样信号，不仅是时间和空间上的浪费，也导致勘探成本较大。基于此，本项目引入新近诞生的压缩感知理论，将地震信号采集和压缩合二为一，融合勘探数据在某些局部位置的已知特征于目标函数，构建更加符合实际情况的自适应压缩感知模型；引入流形学习和主分量分析挖掘现实中勘探数据的关键本质特征，自适应调整变换基函数以获得地震资料的最佳稀疏表示；基于稀疏Haar类正交矩阵的高效算法，构造与变换基不相干的测量矩阵；从最优匹配原子的选择策略和残差信号的更新方式方面对比分析各种算法的重构性能，融合现有几类重构算法的优点并考虑局部先验特征，恰当选择支撑集的大小和优化迭代的步长与次数，设计盲稀疏度下的变步长自适应匹配追踪和罚因子重建算法，在测量次数、重建误差和重建速度之间达到最佳平衡。

中文关键词： 压缩感知；稀疏表示；正交变换；凸优化；重构

英文摘要： Due to the restriction of the complex conditions, the incomplete seismic data often affects the subsequent processing and interpretation of the signal, and the final judgment of oil and gas. The traditional reconstruction methods require the rate of the sampled signal twice more than the highest signal frequency, it not only is a waste of time and space, but also leads to the increment of exploration costs. For this reason, this project will introduce the compressed sensing to the seismic signal acquisition and compression at the same time, construct adaptive compressed sensing model by integrating a small amount of known features of the seismic signals in certain local positions to the objective function, adaptively adjust the transform basis functions to obtain the best sparse representation by the introduction of manifold learning and principal component analysis to mine the key essential features of the seismic data. Meanwhile, this project will develop more flexible signal measurement matrix which is irrelevant to the transform base based on the efficient algorithm of sparse Haar type orthogonal matrix, compare the reconstruction performance of various algorithms in terms of the selection strategy of optimal matching atomic and the variation means of the residual signal, integrate the existing types of reco

英文关键词： compressive sensing；sparse representation；orthogonal transform；convex optimization；reconstruction