ptwt 0.0.14

Differentiable and gpu enabled fast wavelet transforms in PyTorch

Welcome to the PyTorch wavelet toolbox. This package implements:

• the fast wavelet transform (fwt) implemented in wavedec.

• the inverse fwt can be used by calling waverec.

• the 2d fwt is called wavedec2

• and inverse 2d fwt waverec2.

• 1d sparse-matrix fast wavelet transforms with boundary filters.

• 2d sparse-matrix transforms with boundary filters (experimental).

• single and two-dimensional wavelet packet forward transforms.

• adaptive wavelet support (experimental).

This toolbox supports pywt-wavelets. Complete documentation is available: https://pytorch-wavelet-toolbox.readthedocs.io/en/latest/ptwt.html

Installation

Install the toolbox via pip or clone this repository. In order to use pip, type:

$ pip install ptwt

You can remove it later by typing pip uninstall ptwt.

Example usage:

import torch
import numpy as np
import pywt
import ptwt  # use " from src import ptwt " if you cloned the repo instead of using pip.

# generate an input of even length.
data = np.array([0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0])
data_torch = torch.from_numpy(data.astype(np.float32))
wavelet = pywt.Wavelet('haar')

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

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

Sparse-Matrices

In addition to convolution and padding approaches, sparse-matrix-based code with boundary wavelet support is available. Generate 1d sparse matrix forward and backward transforms with the MatrixWavedec and MatrixWaverec classes. Continuing the example above try for example:

# forward
matrix_wavedec = ptwt.MatrixWavedec(wavelet, level=2)
coeff = matrix_wavedec(data_torch)
print(coeff)
# backward
matrix_waverec = ptwt.MatrixWaverec(wavelet, level=2)
rec = matrix_waverec(coeff)
print(rec)

The process for the 2d transforms MatrixWavedec2d, MatrixWaverec2d, works similarly.

Adaptive Wavelets

Experimental code to train an adaptive wavelet layer in PyTorch is available in the examples folder. In addition to static wavelets from pywt,

• Adaptive product-filters

• and optimizable orthogonal-wavelets are supported.

See https://github.com/v0lta/PyTorch-Wavelet-Toolbox/tree/main/examples for a complete implementation.

Testing

The tests folder contains multiple tests to allow independent verification of this toolbox. After cloning the repository, and moving into the main directory, and installing tox with pip install tox run:

$ tox -e py

📖 Citation

If you find this work useful, please consider citing:

@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}
}