Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Data

2026-06-25

AI Summary

This work addresses the challenges of optimizing implicit neural representations with periodic activation functions, which often suffer from instability and spectral bias, hindering effective modeling of multidimensional signals. To overcome these limitations, the authors propose CHOIR, a novel approach that integrates implicit neural representations with generalized Fourier series. CHOIR introduces a Coordinated Harmonic Stacking (CHS) architecture that replaces conventional function composition, thereby enhancing optimization stability in deep networks. Additionally, it incorporates a Perceptual Spectral Calibration (PSC) mechanism that embeds the power-law spectral prior characteristic of natural images, improving physical plausibility. Extensive experiments demonstrate that CHOIR consistently outperforms state-of-the-art methods across diverse multidimensional signal reconstruction tasks, achieving both superior performance and strong generalization capabilities.

Abstract

Implicit neural representation (INR) has emerged as a powerful prior for multi-dimensional data (e.g., multispectral images and videos). However, most INR methods employing periodic activation functions (e.g., Sine) predominantly rely on function composition. This mechanism introduces optimization instability as network depth increases, thereby limiting their performance. Meanwhile, these methods fail to incorporate proper physical priors to effectively alleviate spectrum bias. To address these issues, inspired by the commonalities between deep periodic networks and generalized Fourier series, we propose a novel Calibrated Harmonic Overlaid Implicit Neural Representation (CHOIR). Specifically, we utilize Coordinated Harmonic Superposition (CHS) to replace the conventional function composition used in most INRs, thereby ensuring optimization stability when scaling network depth. Furthermore, we introduce a Perceptual Spectrum Calibration (PSC) to mitigate spectrum bias. This calibration embeds the ubiquitous power-law spectrum prior of natural images and adjusts the globally fixed spectrum towards a physically plausible log-uniform distribution. Extensive experiments on various multidimensional data recovery problems demonstrate that our method achieves superior performance over state-of-the-art approaches. Code is available at https://github.com/chorl0229/CHOIR.

Problem

• Implicit Neural Representation
• Optimization Instability
• Spectrum Bias
• Periodic Activation Functions
• Multi-Dimensional Data

Innovation

• Implicit Neural Representation
• Harmonic Superposition
• Spectrum Calibration
• Optimization Stability
• Power-law Prior