******************************************
Pytorch Wavelet Toolbox (`ptwt`)
******************************************
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Welcome to the PyTorch wavelet toolbox. This package implements discrete-(DWT) as well as continuous-(CWT) wavelet transforms:
- the fast wavelet transform (fwt) via ``wavedec`` and its inverse by providing the ``waverec`` function,
- the two-dimensional fwt is called ``wavedec2`` the synthesis counterpart ``waverec2``,
- ``wavedec3`` and ``waverec3`` cover the three-dimensional analysis and synthesis case,
- ``fswavedec2``, ``fswavedec3``, ``fswaverec2`` and ``fswaverec3`` support separable transformations.
- ``MatrixWavedec`` and ``MatrixWaverec`` implement sparse-matrix-based fast wavelet transforms with boundary filters,
- 2d sparse-matrix transforms with separable & non-separable boundary filters are available,
- ``MatrixWavedec3`` and ``MatrixWaverec3`` allow separable 3D-fwt's with boundary filters.
- ``cwt`` computes a one-dimensional continuous forward transform,
- single and two-dimensional wavelet packet forward and backward transforms are available via the ``WaveletPacket`` and ``WaveletPacket2D`` objects,
- finally, this package provides adaptive wavelet support (experimental).
This toolbox extends `PyWavelets <https://pywavelets.readthedocs.io/en/latest/>`_. In addition to boundary wavelets, we provide GPU and gradient support via a PyTorch backend.
Complete documentation of our Python API is available at: https://pytorch-wavelet-toolbox.readthedocs.io/en/latest
This toolbox is independent work. Meta or the PyTorch team have not endorsed it.
**Installation**
Install the toolbox via pip or clone this repository. In order to use ``pip``, type:
.. code-block:: sh
pip install ptwt
You can remove it later by typing ``pip uninstall ptwt``.
Example usage:
""""""""""""""
**Single dimensional transform**
One way to compute fast wavelet transforms is to rely on padding and
convolution. Consider the following example:
.. code-block:: python
import torch
import numpy as np
import pywt
import ptwt # use "from src import ptwt" for a cloned the repo
# 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'),
wavelet))
The functions ``wavedec`` and ``waverec`` compute the 1d-fwt and its inverse.
Internally both rely on ``conv1d``, and its transposed counterpart ``conv_transpose1d``
from the ``torch.nn.functional`` module. This toolbox also supports discrete wavelets
see ``pywt.wavelist(kind='discrete')``. I have tested
Daubechies-Wavelets ``db-x`` and symlets ``sym-x``, are usually a good starting point.
**Two-dimensional transform**
Analog to the 1d-case ``wavedec2`` and ``waverec2`` rely on
``conv2d``, and its transposed counterpart ``conv_transpose2d``.
To test an example, run:
.. code-block:: python
import ptwt, torch
from scipy import datasets
data = torch.tensor(datasets.face(), dtype=torch.float64)
# permute [H, W, C] -> [C, H, W]
data = data.permute(2, 0, 1)
coefficients = ptwt.wavedec2(face, "haar", level=2, mode="constant")
reconstruction = ptwt.waverec2(coefficients, "haar")
torch.max(torch.abs(face - reconstruction))
**Speed tests**
Speed tests comparing our tools to related libraries are `available <https://github.com/v0lta/PyTorch-Wavelet-Toolbox/tree/main/examples/speed_tests/>`_.
**Boundary Wavelets with Sparse-Matrices**
In addition to convolution and padding approaches,
sparse-matrix-based code with boundary wavelet support is available.
In contrast to padding, boundary wavelets do not add extra pixels at
the edges.
Internally, boundary wavelet support relies on ``torch.sparse.mm``.
Generate 1d sparse matrix forward and backward transforms with the
``MatrixWavedec`` and ``MatrixWaverec`` classes.
Reconsidering the 1d case, try:
.. code-block:: python
import torch
import pywt
import ptwt # use "from src import ptwt" for a cloned the repo
# generate an input of even length.
data = torch.arange(16, dtype=torch.float32)
# forward
matrix_wavedec = ptwt.MatrixWavedec(haar, level=2)
coeff = matrix_wavedec(data)
print(coeff)
# backward
matrix_waverec = ptwt.MatrixWaverec("haar")
rec = matrix_waverec(coeff)
print(rec)
The process for the 2d transforms ``MatrixWavedec2``, ``MatrixWaverec2`` works similarly.
By default, a separable transformation is used.
To use a non-separable transformation, pass ``separable=False`` to ``MatrixWavedec2`` and ``MatrixWaverec2``.
Separable transformations use a 1D transformation along both axes, which might be faster since fewer matrix entries
have to be orthogonalized.
**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/network_compression/ for a complete implementation.
**Testing**
The ``tests`` folder contains multiple tests to allow independent verification of this toolbox.
The GitHub workflow executes a subset of all tests for efficiency reasons.
After cloning the repository, moving into the main directory, and installing ``nox`` with ``pip install nox`` run
.. code-block:: sh
nox --session test
for all existing tests.
Citation
""""""""
If you use this work in a scientific context, please cite the following:
.. code-block::
@article{JMLR:v25:23-0636,
author = {Moritz Wolter and Felix Blanke and Jochen Garcke and Charles Tapley Hoyt},
title = {ptwt - The PyTorch Wavelet Toolbox},
journal = {Journal of Machine Learning Research},
year = {2024},
volume = {25},
number = {80},
pages = {1--7},
url = {http://jmlr.org/papers/v25/23-0636.html}
}
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"description": "******************************************\nPytorch Wavelet Toolbox (`ptwt`) \n******************************************\n\n.. image:: https://github.com/v0lta/PyTorch-Wavelet-Toolbox/actions/workflows/tests.yml/badge.svg \n :target: https://github.com/v0lta/PyTorch-Wavelet-Toolbox/actions/workflows/tests.yml\n :alt: GitHub Actions\n\n.. image:: https://readthedocs.org/projects/pytorch-wavelet-toolbox/badge/?version=latest\n :target: https://pytorch-wavelet-toolbox.readthedocs.io/en/latest/\n :alt: Documentation Status\n\n.. image:: https://img.shields.io/pypi/pyversions/ptwt\n :target: https://pypi.org/project/ptwt/\n :alt: PyPI Versions\n\n.. image:: https://img.shields.io/pypi/v/ptwt\n :target: https://pypi.org/project/ptwt/\n :alt: PyPI - Project\n\n.. image:: https://img.shields.io/pypi/l/ptwt\n :target: https://github.com/v0lta/PyTorch-Wavelet-Toolbox/blob/main/LICENSE\n :alt: PyPI - License\n\n.. image:: https://img.shields.io/badge/code%20style-black-000000.svg\n :target: https://github.com/psf/black\n :alt: Black code style\n\n.. image:: https://static.pepy.tech/personalized-badge/ptwt?period=total&units=international_system&left_color=grey&right_color=brightgreen&left_text=Downloads\n :target: https://pepy.tech/project/ptwt\n\n\nWelcome to the PyTorch wavelet toolbox. This package implements discrete-(DWT) as well as continuous-(CWT) wavelet transforms:\n\n- the fast wavelet transform (fwt) via ``wavedec`` and its inverse by providing the ``waverec`` function,\n- the two-dimensional fwt is called ``wavedec2`` the synthesis counterpart ``waverec2``,\n- ``wavedec3`` and ``waverec3`` cover the three-dimensional analysis and synthesis case,\n- ``fswavedec2``, ``fswavedec3``, ``fswaverec2`` and ``fswaverec3`` support separable transformations.\n- ``MatrixWavedec`` and ``MatrixWaverec`` implement sparse-matrix-based fast wavelet transforms with boundary filters,\n- 2d sparse-matrix transforms with separable & non-separable boundary filters are available,\n- ``MatrixWavedec3`` and ``MatrixWaverec3`` allow separable 3D-fwt's with boundary filters.\n- ``cwt`` computes a one-dimensional continuous forward transform,\n- single and two-dimensional wavelet packet forward and backward transforms are available via the ``WaveletPacket`` and ``WaveletPacket2D`` objects,\n- finally, this package provides adaptive wavelet support (experimental).\n\nThis toolbox extends `PyWavelets <https://pywavelets.readthedocs.io/en/latest/>`_. In addition to boundary wavelets, we provide GPU and gradient support via a PyTorch backend.\nComplete documentation of our Python API is available at: https://pytorch-wavelet-toolbox.readthedocs.io/en/latest\n\nThis toolbox is independent work. Meta or the PyTorch team have not endorsed it.\n\n**Installation**\n\nInstall the toolbox via pip or clone this repository. In order to use ``pip``, type:\n\n.. code-block:: sh\n\n pip install ptwt\n \n\nYou can remove it later by typing ``pip uninstall ptwt``.\n\nExample usage:\n\"\"\"\"\"\"\"\"\"\"\"\"\"\"\n**Single dimensional transform**\n\nOne way to compute fast wavelet transforms is to rely on padding and\nconvolution. Consider the following example: \n\n.. code-block:: python\n\n import torch\n import numpy as np\n import pywt\n import ptwt # use \"from src import ptwt\" for a cloned the repo\n \n # generate an input of even length.\n data = np.array([0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0])\n data_torch = torch.from_numpy(data.astype(np.float32))\n wavelet = pywt.Wavelet('haar')\n \n # compare the forward fwt coefficients\n print(pywt.wavedec(data, wavelet, mode='zero', level=2))\n print(ptwt.wavedec(data_torch, wavelet, mode='zero', level=2))\n \n # invert the fwt.\n print(ptwt.waverec(ptwt.wavedec(data_torch, wavelet, mode='zero'),\n wavelet))\n\n\nThe functions ``wavedec`` and ``waverec`` compute the 1d-fwt and its inverse.\nInternally both rely on ``conv1d``, and its transposed counterpart ``conv_transpose1d``\nfrom the ``torch.nn.functional`` module. This toolbox also supports discrete wavelets\nsee ``pywt.wavelist(kind='discrete')``. I have tested\nDaubechies-Wavelets ``db-x`` and symlets ``sym-x``, are usually a good starting point. \n\n**Two-dimensional transform**\n\nAnalog to the 1d-case ``wavedec2`` and ``waverec2`` rely on \n``conv2d``, and its transposed counterpart ``conv_transpose2d``.\nTo test an example, run:\n\n\n.. code-block:: python\n\n import ptwt, torch\n from scipy import datasets\n\n data = torch.tensor(datasets.face(), dtype=torch.float64)\n # permute [H, W, C] -> [C, H, W]\n data = data.permute(2, 0, 1)\n coefficients = ptwt.wavedec2(face, \"haar\", level=2, mode=\"constant\")\n reconstruction = ptwt.waverec2(coefficients, \"haar\")\n torch.max(torch.abs(face - reconstruction))\n\n\n**Speed tests**\n\nSpeed tests comparing our tools to related libraries are `available <https://github.com/v0lta/PyTorch-Wavelet-Toolbox/tree/main/examples/speed_tests/>`_.\n\n\n**Boundary Wavelets with Sparse-Matrices**\n\nIn addition to convolution and padding approaches,\nsparse-matrix-based code with boundary wavelet support is available.\nIn contrast to padding, boundary wavelets do not add extra pixels at \nthe edges.\nInternally, boundary wavelet support relies on ``torch.sparse.mm``.\nGenerate 1d sparse matrix forward and backward transforms with the\n``MatrixWavedec`` and ``MatrixWaverec`` classes.\nReconsidering the 1d case, try:\n\n.. code-block:: python\n\n import torch\n import pywt\n import ptwt # use \"from src import ptwt\" for a cloned the repo\n \n # generate an input of even length.\n data = torch.arange(16, dtype=torch.float32)\n # forward\n matrix_wavedec = ptwt.MatrixWavedec(haar, level=2)\n coeff = matrix_wavedec(data)\n print(coeff)\n # backward \n matrix_waverec = ptwt.MatrixWaverec(\"haar\")\n rec = matrix_waverec(coeff)\n print(rec)\n\n\nThe process for the 2d transforms ``MatrixWavedec2``, ``MatrixWaverec2`` works similarly.\nBy default, a separable transformation is used.\nTo use a non-separable transformation, pass ``separable=False`` to ``MatrixWavedec2`` and ``MatrixWaverec2``.\nSeparable transformations use a 1D transformation along both axes, which might be faster since fewer matrix entries\nhave to be orthogonalized.\n\n\n**Adaptive Wavelets**\n\nExperimental code to train an adaptive wavelet layer in PyTorch is available in the ``examples`` folder. In addition to static wavelets\nfrom pywt,\n\n- Adaptive product-filters\n- and optimizable orthogonal-wavelets are supported.\n\nSee https://github.com/v0lta/PyTorch-Wavelet-Toolbox/tree/main/examples/network_compression/ for a complete implementation.\n\n\n**Testing**\n\nThe ``tests`` folder contains multiple tests to allow independent verification of this toolbox.\nThe GitHub workflow executes a subset of all tests for efficiency reasons. \nAfter cloning the repository, moving into the main directory, and installing ``nox`` with ``pip install nox`` run\n\n.. code-block:: sh\n\n nox --session test\n\n\n\nfor all existing tests.\n\nCitation\n\"\"\"\"\"\"\"\"\n\nIf you use this work in a scientific context, please cite the following:\n\n.. code-block::\n\n @article{JMLR:v25:23-0636,\n author = {Moritz Wolter and Felix Blanke and Jochen Garcke and Charles Tapley Hoyt},\n title = {ptwt - The PyTorch Wavelet Toolbox},\n journal = {Journal of Machine Learning Research},\n year = {2024},\n volume = {25},\n number = {80},\n pages = {1--7},\n url = {http://jmlr.org/papers/v25/23-0636.html}\n }\n",
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