Additive decomposition of one-dimensional signals using Transformers

Abstract: One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often rely on mathematical models, recent research suggests that applying the latest deep learning models to this problem presents an exciting, unexplored area with promising potential. This work presents a novel method for the additive decomposition of one-dimensional signals. We leverage the Transformer architecture to decompose signals into their constituent components: piece-wise constant, smooth (low-frequency oscillatory), textured (high-frequency oscillatory), and a noise component. Our model, trained on synthetic data, achieves excellent accuracy in modeling and decomposing input signals from the same distribution, as demonstrated by the experimental results.