A clean convergent alternating projections onto convex sets method for data reconstruction

Abstract

Seismic data reconstruction addresses the challenge of accurately restoring incomplete or damaged seismic datasets, which is crucial for subsurface imaging and exploration. The missing data is often due to equipment failure, signal loss, environmental noise, or poor geological conditions. It may also result from limitations in data acquisition, such as sparse sampling and noise interference. This thesis proposes a Clean Convergent alternating Projections onto Convex Sets (CCP) method for data reconstruction. By incorporating an initial value tweaking step into the alternating projections process in the Convergent alternating Projections onto Convex Sets (CP) method, this method aims to reduce ringing noise in the reconstruction results by the CP method. Initially, the traditional CP method and its application in seismic data reconstruction are introduced, highlighting its shortcomings in addressing ringing noise. To overcome this issue, a CCP method based on a non-local means algorithm for initial value tweaking is proposed and applied within the outer loop of the CP method. The theoretical foundation and implementation steps of the CCP method are discussed in detail, and its effectiveness is validated through a series of experiments. The experimental results demonstrate that, compared to the traditional CP method, the CCP method significantly reduces ringing noise and improves the quality of the reconstructed data. Various datasets, including images, 2D seismic section data from the SEAM II Arid model, and 3D seismic model cubes, are used to showcase the reconstruction capabilities of the CCP method in different scenarios. Finally, the thesis provides an in-depth discussion of the CCP method, including intermediate results in the outer loop, the necessity of data preconditioning, and parameter testing, offering a practical set of control parameter settings. The study shows that the CCP method has broad application prospects in data reconstruction, providing valuable references for future research.