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Differentiable and gpu enabled fast wavelet transforms in JAX

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Differentiable and GPU-enabled fast wavelet transforms in JAX.


  • 1d analysis and synthesis transforms are implemented in src/jaxwt/

  • 2d analysis and synthesis transform are part of the src/jaxwt/ module.

  • cwt-function supports 1d continuous wavelet transforms.

  • The WaveletPacket object supports 1d wavelet packet analysis transforms.

  • WaveletPacket2d implements two-dimensional wavelet packet forward transforms.


To install Jax, head over to 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.


The documentation is available at: .

Transform Examples:

One-dimensional fast wavelet transform:

import pywt
import numpy as np;
import jax.numpy as jnp
import jaxwt as jwt
# 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])
wavelet = pywt.Wavelet('haar')

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

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

Two-dimensional fast wavelet transform:

import pywt, scipy.misc
import jaxwt as jwt
import jax.numpy as np
face = np.transpose(scipy.misc.face(), [2, 0, 1]).astype(np.float64)
transformed = jwt.wavedec2(face, pywt.Wavelet("haar"), level=2, mode="reflect")
reconstruction = jwt.waverec2(transformed, pywt.Wavelet("haar"))
np.max(np.abs(face - reconstruction))


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

$ pip install nox
$ git clone
$ cd Jax-Wavelet-Toolbox
$ nox -s test


  • 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

To allow 64-bit precision numbers, a Jax config flag must be set as shown below:

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

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