Adaptive Dictionary Identification Framework and its Application to Sparsity-Optimized Harmonic Noise Separation

Abstract

Coherent noise separation stands as a critical step in seismic data processing. The Morphological Component Analysis (MCA)-based separation method, treating coherent noise and signal as distinct components and representing them sparsely with dictionaries, has found widespread application in the effective suppression of coherent noise. In practice, when constructing effective fixed dictionaries for MCA-based separation methods, a common approach involves conducting numerous experiments to meticulously select appropriate transform basis functions from an extensive dictionary library and tune their parameters. To mitigate time consumption and ensure optimal dictionary construction, we introduce a framework for adaptive identification of the optimal dictionaries used in MCA-based coherent noise separation. Specifically, we initially characterize the notion of a fixed dictionary library, which encompasses dictionaries constructed using various transform basis functions and their corresponding parameters. Then, we present a Relative Sparsity Minimization Problem (RSMP), formulated to identify the optimal fixed dictionaries that lead to minimum relative sparsity within the predefined library. Finally, we design a genetic algorithm to solve RSMP. The optimal dictionaries obtained for representing signal and coherent noise, respectively, are applied to MCA-based coherent noise separation. Synthetic and field data examples demonstrate the effectiveness of the proposed method.