Research On Seismic Data Denoising Method Based On Manifold Dictionary Learning

During seismic acquisition,there are noise such as surface waves,multiple waves and low frequency noise interference,which can directly affect the subsequent processing and interpretation of seismic data.Over the years,many seismic processing software have conducted in-depth research into noise suppression of seismic data and have developed a range of effective algorithms.However,as exploration methods change from 2D to 3D,4D or even5 D,the amount of data in seismic data increases dramatically.Based on the combination of computational accuracy and computational cost,many conventional denoising algorithms can no longer meet the needs of subsequent seismic data processing and interpretation.In contrast,the theoretical framework of compressive sensing has been refined and promoted in recent years.Sparse representation,that is dictionary learning,has entered the geophysical field with its excellent feature extraction capability as well as computational power.Dictionary learning takes advantage of the sparsity of seismic data to provide the sparse representation of the data.Unlike traditional fixed-base transform methods such as wavelet transform and curvelet transform,learning dictionary has more flexible sparse representation of seismic data.Updating the dictionary is an extremely important part of the dictionary learning process.The K-SVD algorithm is a commonly used dictionary upgrade algorithm due to its flexible and efficient sparse representation capability.In this paper,a discrete cosine transform dictionary,a homogeneous real data learning dictionary and a non-homogeneous real data learning dictionary are designed as the initial dictionaries to perform real data denoising experiments.The experimental results demonstrate the differences in the adaptive learning of dictionary atoms,the denoising effect on the data and the computational efficiency of denoising for the different initial dictionaries.Finally,the setting method of the initial dictionary is discussed,and the suggestion of using the dictionary learning to suppress the noise of real data is put forward.The K-SVD dictionary learning algorithm does not consider the channel correlation of seismic data.It is not capable of sparse representation of 3D or even higher dimensional seismic data,and is not computationally efficient.Manifold learning is widely used in the fields of pattern recognition and image processing.Because the algorithm has the excellent feature extraction and sample inscription capabilities,which can efficiently achieve dimensionality reduction of high-dimensional data.This paper proposes a method to denoise seismic data based on manifold dictionary learning from the perspective of manifold projection mapping and mathematical optimization.The seismic data and the dictionary are sparsely encoded on the projection mapping onto Grassmann Manifolds to achieve a better sparse representation while also convex optimization of objective function to accelerate convergence and obtain a globally optimal solution.The dictionary updating process is distinguished from using K-SVD and uses the Lagrange multiplier method instead.Its advantage is reducing the computational complexity by converting the minimax problem to an eigenvalue problem for solution.The dictionary learning algorithm based on Grassmann Manifolds is used to denoise the 3D seismic data.The results of the denoising are analyzed and the effectiveness of the method and its applicability are discussed.