Orthogonal dictionary learning based on l₄-Norm maximisation for seismic data interpolation

Abstract

Due to geological conditions, acquisition environment, and economic restrictions, acquired seismic data are often incomplete and irregularly distributed, and this affects subsequent migration imaging and inversion. Sparse constraint-based methods are widely used for seismic data interpolation, including fixed-base transform and dictionary learning. Fixed-base transform methods are fast and simple to implement, but the basis function needs to be pre-selected. The dictionary learning method is more adaptive, and provides a means of learning the sparse representation from corrupted data. K-singular value decomposition (K-SVD) is a classical dictionary learning method that combines sparse coding and dictionary updating iteratively. However, the dictionary atoms are updated column-by-column, leading to high computational complexity due to long SVD calculation times. In this study, we evaluated the dictionary learning method via l₄-norm maximisation using an orthogonal dictionary, which is different from the traditional l₀-norm or l₁-norm minimisation, and interpolated the missing traces in the projection onto convex sets (POCS) framework. The optimal objection function is convex, but can be solved using a simple and efficient Matching, Stretching and Projection (MSP) algorithm, which greatly reduces the dictionary learning time. Numerical experiments using synthetic and field data demonstrate the effectiveness of the proposed method.

KEYWORDS:

• Seismic data interpolation
• dictionary learning
• K-SVD
• l₄-norm maximisation
• orthogonal dictionary

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is financially supported by the National Natural Science Foundation of China (grant number 42274172).