Additive decomposition of one-dimensional signals using Transformers

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 very ill-posed inverse problem represents 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: piecewise constant, smooth (trend), highly-oscillatory, and noise components. 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.