TRIDENT: The Nonlinear Trilogy for Implicit Neural Representations

Zhenda Shen1,2*
Yanqi Cheng1*
Raymond H Chan2
Pietro Liò1
Carola-Bibiane Schönlieb1
Angelica I. Aviles-Rivero1

1University of Cambridge       2 City University of Hong Kong (CityU)
affiliations

[Paper]
This is a website made for TRIDENT: The Nonlinear Trilogy for Implicit Neural Representations.

Abstract

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.

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Paper and Supplementary Material


Zhenda Shen*, Yanqi Cheng*, Raymond H. Chan, Pietro Liò, Carola-Bibiane Schönlieb, Angelica I Aviles-Rivero.
TRIDENT: The Nonlinear Trilogy for Implicit Neural Representations
(hosted on ArXiv)

[Bibtex]

Acknowledgements

ZS acknowledges support from the Department of Mathematics, College of Science, CityU, and HKASR reaching out award. YC and AIAR greatly acknowledge funding from the Cambridge Centre for Data-Driven Discovery and Accelerate Programme for Scientific Discovery, made possible by a donation from Schmidt Futures. RHC acknowledges support from HKRGC GRF grants CityU1101120 and CityU11309922 and CRF grant C1013-21GF. AIAR acknowledges support from CMIH (EP/T017961/1) and CCIMI, University of Cambridge. This work was supported in part by Oracle Cloud credits and related resources provided by Oracle for Research. Also, EPSRC Digital Core Capability. CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC advanced career fellowship EP/V029428/1, EPSRC grants EP/S026045/1 and EP/T003553/1, EP/N014588/1, EP/T017961/1, the Wellcome Innovator Awards 215733/Z/19/Z and 221633/Z/20/Z, the European Union Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute.