ABSTRACT
The seismic interpolation problem can be deemed as a compressive sensing (CS) problem, because seismic acquisition is the sampling processing of seismic data. Based on CS theory, the sparse transform-based method and the matrix/tensor completion method change the seismic interpolation problem into sparse optimization problems. This chapter focuses on these two interpolation methods. It introduces basic CS theory, illustrates the mathematical models of seismic interpolation based on these methods and outlines an efficient algorithm for seismic interpolation. The rank number in the multichannel singular spectrum analysis (MSSA) method plays the role of regularization. In order to get stable solutions, it needs to be reduced gradually over iterations. Therefore, the idea of the MSSA is similar to that of the thresholding methods. The chapter discusses some sparse optimization methods that can solve the induced sparse optimization models efficiently. It provides synthetic and experimental tests based on some proposed models and methods to show the efficiency of CS theory and sparse optimization.
