Adaptive dictionary identification framework and its application to sparsity-optimized harmonic noise separation

Coherent noise separation stands as a crucial step in seismic data processing. The morphological component analysis (MCA)-based separation method, which treats coherent noise and signal as distinct components and represents them sparsely with dictionaries, has been widely adopted for noise suppression. Typically, constructing effective fixed dictionaries for MCA-based methods involves necessary expert knowledge to meticulously select appropriate transform basis functions from an extensive dictionary library and fine-Tune their parameters. To reduce time consumption and ensure optimal dictionary construction, we introduce an adaptive framework for identifying optimal dictionaries used in MCA-based coherent noise separation. Initially, we define a fixed dictionary library comprising dictionaries constructed using various transform basis functions with their corresponding parameters. Subsequently, we formulate a relative sparsity minimization problem (RSMP) to identify the optimal fixed dictionaries that minimize relative sparsity within this predefined library. Finally, we design a genetic algorithm to solve RSMP. The identified dictionaries are then applied to MCA-based coherent noise separation. Synthetic and field data examples demonstrate the effectiveness of our method.