Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA
This work addresses the challenge of applying low-rank decompositions to continuous and irregularly sampled signals, which is incremental as it extends existing PCA and ICA techniques to a new domain.
The authors tackled the problem of generalizing PCA and ICA to continuous-time signals by introducing an implicit neural representation framework, enabling decomposition of irregularly sampled data where traditional methods fail.
We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to learn numerical approximations to solve the problem. Modeling signals as continuous-time stochastic processes, we unify the approaches to both the PCA and ICA problems in the continuous setting through a contrast function term in the network loss, enforcing the desired statistical properties of the source signals (decorrelation, independence) learned in the decomposition. This extension to a continuous domain allows the application of such decompositions to point clouds and irregularly sampled signals where standard techniques are not applicable.