Novel sparse decomposition with adaptive evolutionary atoms for nonstationary signal extraction

Existing sparse decomposition techniques often rely on over-complete dictionaries and extensive prior knowledge, leading to slow computation and low efficiency. This paper introduces a novel sparse decomposition method, Adaptive Evolutionary Atomic Sparse Decomposition (AEA-SD). A general atom (g-atom) is designed to accommodate various typical signals, accompanied by an adaptive atom-based automatic target signal localization algorithm. To accelerate convergence, a fast sparse decomposition method based on Bat algorithm is developed, which eliminates the reliance on redundant dictionaries. The performance of AEA-SD is verified by using magnetotelluric (MT) data. Experimental results demonstrate that AEA-SD reduces CPU usage by over 30% compared to traditional algorithms and enhances signal extraction accuracy by at least 58%, 46%, and 58% in low, middle, and high frequency bands, respectively. Furthermore, the method's adaptability makes it applicable to diverse scenarios requiring the removal of complex background noise from sensor signals.