TRIDENT: The Nonlinear Trilogy for Implicit Neural Representations
Zhenda Shen Yanqi Cheng Raymond H. Chan Pietro Liò Carola-Bibiane Schönlieb Angelica I Aviles-Rivero
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.