# WIRE: Wavelet Implicit Neural Representations

**Authors:** Vishwanath Saragadam, Daniel LeJeune, Jasper Tan, Guha Balakrishnan, Ashok Veeraraghavan, Richard G. Baraniuk  
**arXiv:** [2301.05187](https://arxiv.org/abs/2301.05187)  
**Date:** 2023-01-05  
**Summary page:** https://www.summarizepaper.com/en/paper/2301.05187v1/

## Key points

- Implicit neural representations (INRs) have advanced in vision-related applications
- Choice of nonlinear activation function impacts INR performance
- Wavelet Implicit Neural Representation (WIRE) developed for improved accuracy and robustness
- WIRE uses Gabor wavelet activation function for optimal space-frequency concentration and image representation biases
- WIRE addresses tradeoff between accuracy and robustness seen in current models
- WIRE sets new benchmarks in accuracy, training time efficiency, and robustness across various vision tasks
- Leveraging wavelet atoms for precise and resilient image representation
- Wavelet-based approaches more effective than traditional Fourier methods for natural image complexities

## Summary

The field of implicit neural representations (INRs) has seen significant advancements in various vision-related applications. One key factor influencing the performance of INRs is the choice of nonlinear activation function used in their multilayer perceptron networks. While a wide range of nonlinearities have been explored, current INRs that prioritize high accuracy often struggle with poor robustness to factors like signal noise and parameter variation. Drawing inspiration from harmonic analysis, a team of researchers led by Vishwanath Saragadam developed a new type of INR called Wavelet Implicit Neural Representation (WIRE). WIRE utilizes a continuous complex Gabor wavelet activation function known for its optimal concentration in space-frequency and excellent biases for image representation. This unique approach addresses the tradeoff between accuracy and robustness commonly observed in existing models. Through extensive experiments covering tasks such as image denoising, inpainting, super-resolution, computed tomography reconstruction, image overfitting, and novel view synthesis using neural radiance fields, WIRE has emerged as a groundbreaking solution setting new benchmarks in terms of accuracy, training time efficiency, and robustness. By leveraging wavelet atoms that are finely tuned for representing images with precision and resilience, WIRE showcases superior performance across a diverse range of vision tasks. The research team's findings highlight the limitations of traditional Fourier methods in capturing the complexities present in natural images and emphasize the effectiveness of wavelet-based approaches for achieving more concise and reliable signal representations. With WIRE paving the way for enhanced capabilities in handling challenging vision tasks, this innovative framework represents a significant leap forward in the realm of implicit neural representations.