WIRE: Wavelet Implicit Neural Representations

We propose a new nonlinearity for implicit neural representations (INRs) based on the continuous complex Gabor wavelet that has high representation capacity for visual signals. (a) visualizes two commonly used nonlinearities: SIREN with sinusoidal nonlinearity and Gaussian nonlinearity, and WIRE that uses a continuous complex Gabor wavelet. WIRE benefits from the frequency compactness of sine, and spatial compactness of a Gaussian nonlinearity. (b) shows error maps for approximating an image with strong edges. SIREN results in global ringing artifacts while Gaussian nonlinearity leads to compact but large error at edges. WIRE produces results with the smallest and most spatially compact error. This enables WIRE to learn representations rapidly and accurately, while being robust to noise and undersampling of data.

Paper: https://arxiv.org/abs/2301.05187

Instructions

Data

Download image and occupancy examples from here. Place it in path/to/this/folder/data/.

Requirements

check requirements.txt. This code was tested on python 3.8 in both Windows and Linux environments. Requirements file generated in Linux environment but should work similarly in a Windows environment.

Denoising images with WIRE

Check wire_image_denoise.py for denoise an image. We have included an example image from div2k in data/parrot.png.

Representing pointclouds with WIRE

Check wire_occupancy.py for fitting a 3D shape with occupancy information. For simplicity, we have included occupancy volume of Thai statue with regular sampling over 512x512x512 cube.

Multi-image super-resolution with WIRE

Check wire_multi_sr.py for performing super-resolution with multiple images captured with small motion between the frames. We have included an example image data/kodak.png for this script.

Computed tomographic reconstruction with WIRE

Please check wire_ct.py for reconstructing images from computed tomographic measurements. We have included an example image data/chest.png.

Information about individual files

1. wire_image_denoise.py : Runs training script for a single image

2. wire_occupancy.py: Runs training script for a uniformly sampled occupancy of a 3D shape

3. wire_multi_sr.py: Runs training script for solving multi-image super-resolution

4. wire_ct.py : Runs training script for solving the computed tomography problem

5. requirements.txt: All requirements for running scripts in this folder

6. modules: Contains functions to run the training scripts:

   a. lin_inverse.py: Includes forward operator for computed tomography

   b. motion.py: Contains functions for handling multi-image super resolution data generation

   c. models.py: Common wrapper to instantiate all INR models

   d. utils.py: Miscellaneous utilities

   e. volutils.py: Utilities for handling volume signals

   f. wire.py: Contains definitions for implementing WIRE.

   g. wire2d.py: Contains definition for 2d wire as shown in section 4.4 in the main paper.

   h. mfn.py: Contains multiplicative frequency networks implementation by the authors of the original paper

   i. relu.py: Contains relu and positional encoding implementation

   j. siren.py: Contains original implementation of SIREN

   k. gauss.py: Contains implementation of Gaussian nonlinearity

Cite

@inproceedings{saragadam2022wire,
  title={WIRE: Wavelet Implicit Neural Representations},
  author={Saragadam, Vishwanath and LeJeune, Daniel and Tan, Jasper and Balakrishnan, Guha and Veeraraghavan, Ashok and Baraniuk, Richard G},
  booktitle={arXiv preprint arXiv:2301.05187}
  year={2022}
}