Seismic data reconstruction via weighted nuclear-norm minimization

Abstract

The low-rank matrix completion theory based on nuclear-norm minimization is becoming increasingly popular in practice, and has been applied to seismic data reconstruction of missing traces. In this paper, we investigate the weighted nuclear-norm minimization model on low-rank seismic texture matrix which is obtained with a designed texture-patch pre-transformation. Unlike the previous nuclear-norm model that treats all singular values of the seismic data matrix equally, the weighted nuclear-norm model, based on the idea of iterative reweighting, makes a closer approximation to the ‘counting rank function’ and can promote the low-rank matrices. We apply weighted spectral soft-thresholding iterative scheme and weighted iterative supported detection method to solve the weighted model. Experimental study on synthetic and real seismic data shows that high-quality reconstruction can be obtained by the weighted low-rank methods.