Paper ID: 2311.13610

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.

Submitted: Nov 21, 2023