Additive decomposition of one-dimensional signals using Transformers

Additive decomposition of one-dimensional signals is a well-studied and widespread technique, as it turns out to be, in various scientific fields, a very useful pre-processing step. The various techniques for decomposition are mostly based on mathematical models; a review of the state of the art found that the use of the latest deep learning models to tackle this problem is an area that has yet to be explored. In this thesis, we propose a method to deal with the additive decomposition of one-dimensional signals using the Transformer architecture to decompose signals into piece-wise constant, smooth (low-frequency oscillatory), texture (high-frequency oscillatory) components, and a noise realization. The experimental results obtained show that our model, trained on synthetic data, is capable of modeling and decomposing with excellent fidelity the components that constitute the input signal for signals belonging to the same distribution of the training data.