Implicit neural representations (INRs) have garnered significant interest recently for their ability to model complex, high-dimensional data without explicit parameterisation. In this work, we introduce TRIDENT, a novel function for implicit neural representations characterised by a trilogy of nonlinearities. Firstly, it is designed to represent high-order features through order compactness. Secondly, TRIDENT efficiently captures frequency information, a feature called frequency compactness. Thirdly, it has the capability to represent signals or images such that most of its energy is concentrated in a limited spatial region, denoting spatial compactness. We demonstrated through extensive experiments on various inverse problems that our proposed function outperforms existing implicit neural representation functions.
@article{arxiv.2311.13610,
title = {TRIDENT: The Nonlinear Trilogy for Implicit Neural Representations},
author = {Zhenda Shen and Yanqi Cheng and Raymond H. Chan and Pietro Liò and Carola-Bibiane Schönlieb and Angelica I Aviles-Rivero},
journal= {arXiv preprint arXiv:2311.13610},
year = {2023}
}