Construction Method of Sparse Dictionary for Multi-Order FRFT Domain Feature Fusion

Abstract

Reverberation constitutes a primary source of interference for active sonar signals, particularly the intense reverberation originating from reflections of the incident signal. Sharing the same generation mechanism as the target echo, it severely hampers the extraction and analysis of the target signal. To enhance signal processing capabilities under strong reverberation, this paper proposes a sparse dictionary construction method based on multi-order fractional Fourier transform (FRFT) domain feature fusion. This method exploits the distinctive characteristics exhibited by target echoes and strong reverberation signals across different fractional transform domains to discriminate between them. It constructs sparse sub-dictionaries using these distinct fractional orders, trains the weights of each sub-dictionary via an adaptive gradient optimization strategy to achieve sparse representation of the signal, suppresses strong interference in the sparse domain, and reconstructs the target signal through a reconstruction process, thereby achieving the goal of extracting the target signal while suppressing strong interference. Results from processing lake trial data demonstrate that the proposed method can effectively extract target echo signals amidst strong reverberation, with the signal-to-reverberation ratio improvement consistently no less than 2.1 dB and reaching up to 15.6 dB. This method provides an effective approach for the processing and analysis of weak underwater signals.