Simultaneous denoising and interpolation of 2D seismic data using data-driven non-negative dictionary learning

As a major concern, the existence of unwanted energy and missing traces in seismic data acquisition can degrade interpretation of such data after processing. Instead of analytical dictionaries, data-driven dictionary learning (DDL) methods as a flexible framework for sparse representation, are dedicated to the problem of denoising and interpolation. Due to their meaningful geometric repetitive structures, seismic data are intrinsically low-rank in the time-space domain. On the other hand, noise and missing traces increase the rank of the noisy data. Therefore, the clean data, unlike noise and missing traces, can be modeled as a linear combination of a few elements from a learned dictionary. In this paper, a parts-based 2D DDL scheme is introduced and evaluated for simultaneous denoising and interpolation of seismic data. A special case of versatile non-negative matrix factorization (VNMF) is used to learn a dictionary. In VNMF, smoothness constraint can improve interpolation, and sparse coding helps improving denoising. The proposed method is tested on synthetic and real-field seismic data for simultaneous denoising and interpolation. Through experimental results, the proposed method is determined to be an effective and robust tool that preserves significant components of the signal. Comparison with four state-of-the-art methods further verifies its superior performance.