Jax Wavelet Toolbox (jaxwt)

Differentiable and GPU-enabled fast wavelet transforms in JAX.

Features

• wavedec and waverec implement 1d analysis and synthesis transforms.
• Similarly, wavedec2 and waverec2 provide 2d transform support.
• The cwt-function supports 1d continuous wavelet transforms.
• The WaveletPacket object supports 1d wavelet packet transforms.
• WaveletPacket2d implements two-dimensional wavelet packet transforms.
• swt and iswt allow 1d-stationary transformations.

This toolbox extends PyWavelets. We additionally provide GPU and gradient support via a Jax backend.

Installation

To install Jax, head over to https://github.com/google/jax#installation and follow the procedure described there. Afterward, type pip install jaxwt to install the Jax-Wavelet-Toolbox. You can uninstall it later by typing pip uninstall jaxwt.

Documentation

Complete documentation of all toolbox functions is available at readthedocs.

Transform Examples:

To compute a one-dimensional fast wavelet transform, consider the code snippet below:

import jax.numpy as jnp
import jaxwt as jwt

import pywt
import numpy as np;

# generate an input of even length.
data = jnp.array([0., 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0])

# compare the forward fwt coefficients
print(pywt.wavedec(np.array(data), 'haar', mode='zero', level=2))
print(jwt.wavedec(data, 'haar', mode='zero', level=2))

# invert the fwt.
print(jwt.waverec(jwt.wavedec(data, 'haar', mode='zero', level=2),
                  'haar'))

The snipped also evaluates the pywt implementation to demonstrate that the coefficients are the same. Use jaxwt if you require gradient or GPU support.

The process for two-dimensional fast wavelet transforms works similarly:

import jaxwt as jwt
import jax.numpy as jnp
from scipy.datasets import face

image = jnp.transpose(
    face(), [2, 0, 1]).astype(jnp.float32)
transformed = jwt.wavedec2(image, "haar",
                           level=2, mode="reflect")
reconstruction = jwt.waverec2(transformed, "haar")
jnp.max(jnp.abs(image - reconstruction))

jaxwt allows transforming batched data. The example above moves the color channel to the front because wavedec2 transforms the last two axes by default. We can avoid doing so by using the axes argument. Consider the batched example below:

import jaxwt as jwt
import jax.numpy as jnp
from scipy.datasets import face

image = jnp.stack(
    [face(), face(), face()], axis=0
     ).astype(jnp.float32)
transformed = jwt.wavedec2(image, "haar",
                           level=2, mode="reflect",
                           axes=(1,2))
reconstruction = jwt.waverec2(transformed, "haar", axes=(1,2))
jnp.max(jnp.abs(image - reconstruction))

For more code examples, follow the documentation link above or visit the examples folder.

Testing

Unit tests are handled by nox. Clone the repository and run it with the following:

$ pip install nox
$ git clone https://github.com/v0lta/Jax-Wavelet-Toolbox
$ cd Jax-Wavelet-Toolbox
$ nox -s test

Goals

• In the spirit of Jax, the aim is to be 100% pywt compatible. Whenever possible, interfaces should be the same results identical.

64-Bit floating-point numbers

If you need 64-bit floating point support, set the Jax config flag:

from jax.config import config
config.update("jax_enable_x64", True)

Citation

If you use this work in a scientific context, please cite the following:

@phdthesis{handle:20.500.11811/9245,
  urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-63361,
  author = {{Moritz Wolter}},
  title = {Frequency Domain Methods in Recurrent Neural Networks for Sequential Data Processing},
  school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
  year = 2021,
  month = jul,
  url = {https://hdl.handle.net/20.500.11811/9245}
}