Seismic Data Denoising And Reconstruction Based On Compressive Sensing And Dictionary Learning

In the field acquisition process,affected by the complicated construction conditions,the acquisited effective signal may be mixed into or even suppressed by the noise,so that the signalto-noise ratio of the seismic data has been reduced.In addition,due to the impact of the forbidden area and the obstacles on the construction,acquisited data may be irregular.All these condition will affect the follow-up processing work.Therefore,suppress noise form noisy data and reconstruct irregular data to make seismic data regular and noise free is one of the most important problems in seismic data processing.Compressed sensing theory is a kind of signal processing theory which is born in recent years and breaks the limitation of traditional sampling theorem.It uses the sparsity of signal,can transform the signal reconstruction problem into an optimization problem by design a suitable measurement matrix so that the original signal can be recovered from the sampled signal with a higher probability even if the sampling theorem is not satisfied.In this paper,under the framework of compressive sensing theory,we introduce three components of compressive sensing: the sparse representation of signals,the design of measurement matrix and the design of restoration algorithm.The three construction methods including sparse dictionary.The basic theoretical framework including three construction methods of sparse dictionary,the constraints of measurement matrix and two main categories of recovery algorithm are expounded.The seismic data denoising method based on dictionary learning is one of the research contents of this paper.The denoising method of seismic data based on dictionary learning is better than the denoising method of seismic data based on mathematical transformation.However,the classical K-SVD algorithm has low efficiency for denoising.In this paper,the KSVD algorithm is improved in two stages of dictionary updating and sparse coding,and a seismic data denoising method based on Sparse K-SVD algorithm is proposed.The feasibility and effectiveness of the method are proved in numerical experiments.Seismic data reconstruction method is another research content of this paper.Numerical experiments show that the strategy of sparse representation of seismic data by morphological component analysis makes the reconstruction effect based on this method better than the single transform domain seismic data reconstruction method.Because the selection of different component sparse dictionaries determines the efficiency and accuracy of reconstruction in the morphological component analysis method,so in this paper we combine the Shearlet dictionary which has excellent sparse representation ability and adaptive dictionary obtained by dictionary learning and propose a method of seismic data reconstruction based on dictionary learning and morphological component analysis.The numerical experiments prove the superiority of this method.