低秩稀疏重建分析的边缘检测方法

Edge detection method for low-rank sparse reconstruction analysis

边缘检测方法众多,并取得了很好的应用效果,但不同方法有其自身的不足和边缘检测能力的限制,特别是对噪声干扰、多边缘干涉及弱小目标边缘的检测效果不理想。为此,首先分析断层边缘和缝洞边缘的空间分布特征,根据断层边缘和缝洞边缘的地震响应特征,把低秩稀疏分析理论引入边缘检测,研究边缘信息、背景信息及噪声信息的低秩稀疏分解与重建;为了提高边缘检测能力和分辨率,在压缩感知稀疏表示基础上,对地震资料进行深度稀疏化表示,结合向量稀疏表示和矩阵稀疏表示,通过低秩稀疏分析理论,形成一种全新的边缘检测方法——低秩稀疏重建分析的边缘检测方法。具体步骤为:(1)地震资料平稳小波分解;(2)多尺度小波系数优化;(3)根据多尺度优化小波系数建立张量矩阵并进行建模;(4)张量矩阵奇异值分解;(5)矩阵奇异值低秩优化;(6)多尺度双稀疏和双优化结果融合与重建。模型分析和实际资料应用效果分析表明:所提方法的抗噪性、适用性较强,对于断层和缝洞边缘具有较好的刻画能力。

Many edge detection methods can achieve good application results.However,these methods have their shortcomings and limited edge detection ability,especially the unsatisfying effects of edge detection for noise interference,multi-edge interference,and weak small targets.Therefore,the spatial distribution characteristics of fault,fracture,and cave edges are analyzed.According to the seismic response characteristics of those edges,the low-rank sparse analysis theory is introduced into edge detection to study the low-rank sparse decomposition and reconstruction of edge information,background information,and noise information.For the improvement of the edge detection ability and resolution,the in-depth sparse representation of seismic data is carried out on the basis of the compressed sensing sparse representation.Given the vector sparse representation and matrix sparse representation,a new edge detection method,i.e.,an edge detection method for low-rank sparse reconstruction analysis,is formed through the low-rank sparse analysis theory.The specific steps are as follows:First,the seismic data is decomposed into stationary wavelets.Second,multiscale wavelet coefficients are optimized.Then,the tensor matrix is established and modeled according to the multi-scale optimized wavelet coefficients.Fourth,the singular values of the tensor matrix are decomposed.Fifth,low-rank optimization of those singular values is conducted.Finally,the multi-scale double sparse and double optimization results are fused and reconstructed.The model analysis and the analysis of practical data application effect show that the proposed method has strong noise resistance and applicability and is capable of effectively depicting the edges of faults,fractures,and caves.