Reconstruction of seismic data with missing traces based on optimized Poisson Disk sampling and compressed sensing

Abstract

In seismic exploration, challenges posed by the collection environment often lead to incomplete or irregular seismic data. Fortunately, Compressed Sensing theory provides the possibility of reconstructing under-sampled data. One of the most important aspects of applying this theory is selection of an appropriate sampling method. In this paper, we propose a seismic data reconstruction method based on optimized Poisson Disk sampling under Compressed Sensing. First, K-Singular Value Decomposition is used to train the seismic sample data and obtain an overcomplete dictionary which can be used to sparsely represent the missing seismic data. Then, after using the optimized Poisson Disk sampling method to compress the seismic data, the missing seismic data are restored by the orthogonal matching pursuit algorithm. The results of experiments show that, unlike the traditional Gaussian random sampling and Poisson Disk sampling methods, the proposed method preserves the uniformity of the sampling points while maintaining the sampling randomness, resulting in improved reconstruction results.