filterbanks 0.0.1

Filter Banks and Multiresolution Transform Layers

filterbanks: Filter Banks and Multiresolution Transform Layers

filterbanks provides TensorFlow/Keras layers for multiresolution and geometric filter banks.

Capabilities

• DCT2D / IDCT2D
• MultiLevelLiftingDWT1D_K
• MultiLevelLiftingDWT2D_K
• MultiLevelLiftingDWT3D_K
• LapPyrAnalysis / LapPyrSynthesis
• MonogenicPyramid2D
• SteerablePyramid2D
• Scattering2D
• WaveAtoms2DAnalysis / WaveAtoms2DSynthesis
• WignerVille1D
• filterbanks.tileviewer for tiling plots

Limitations

• Some layers are analysis-only and do not include a synthesis inverse.
• Exact perfect reconstruction applies only to paired forward/inverse classes where provided.
• Optional viewer and probe utilities may require extra packages such as matplotlib.

Installation

pip install filterbanks

Transform References

Transform	Class / Layer	Original paper
DCT	DCT2D, IDCT2D	Ahmed, Natarajan, Rao, Discrete Cosine Transform, IEEE Trans. Computers, 1974
Monogenic Pyramid	MonogenicPyramid2D	Felsberg, Sommer, The monogenic signal, IEEE Trans. Signal Processing, 2001
Laplacian Pyramid	LapPyrAnalysis, LapPyrSynthesis	Burt, Adelson, The Laplacian Pyramid as a Compact Image Code, IEEE Trans. Communications, 1983
DWT / Wavelets	MultiLevelLiftingDWT1D_K, MultiLevelLiftingDWT2D_K, MultiLevelLiftingDWT3D_K	Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 1988
Lifting DWT	MultiLevelLiftingDWT1D_K, MultiLevelLiftingDWT2D_K, MultiLevelLiftingDWT3D_K	Sweldens, The lifting scheme: A construction of second generation wavelets, SIAM J. Math. Anal., 1998
Steerable Pyramid	SteerablePyramid2D	Freeman, Adelson, The design and use of steerable filters, IEEE TPAMI, 1991
Curvelet	CurveletTransform2D	Candès, Donoho, New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities, Comm. Pure Appl. Math., 2004
Contourlet	ContourletTransform2D	Do, Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Trans. Image Processing, 2005
Wave Atoms	WaveAtoms2DAnalysis, WaveAtoms2DSynthesis	Demanet, Ying, Wave atoms and sparsity of oscillatory patterns, Appl. Comput. Harmon. Anal., 2007
Shearlet	ShearletAnalysis2D, ShearletSynthesis2D	Kutyniok, Labate, Resolution of the wavefront set using continuous shearlets, Trans. Amer. Math. Soc., 2009
Scattering	Scattering2D	Mallat, Group invariant scattering, Comm. Pure Appl. Math., 2012
Wigner-Ville	WignerVille1D	Wigner, On the Quantum Correction for Thermodynamic Equilibrium, 1932; Ville, Application de la notion de signal analytique a la determination de l'amplitude et de la frequence instantanee d'un signal, 1948

Package-Specific Layers

Layer	Note
DWT2DPR	Exact 2D filter-bank operator form used for validation
ShearletPRFBLifting	Trainable shearlet PRFB layers implemented in this package
DirectionalLiftingNSDL	Trainable nonsubsampled directional lifting layers implemented in this package

Minimal Example

import tensorflow as tf
from filterbanks import MultiLevelLiftingDWT2D_K

x = tf.random.normal([1, 64, 64, 1])
layer = MultiLevelLiftingDWT2D_K(levels=2, preset="haar")

pyr = layer(x)
y = layer.synth(*pyr)

print(x.shape, y.shape)

Tiling Viewer

python -m filterbanks.tileviewer.main_viewer --transform contourlet --levels 3 --Ks 4 8 8 --kappas 64 64 64 --H 256 --W 256 --save Figs/contourlet_tiling.png

Citation

This software is released for broad research, educational, and engineering use. If this package helps your work, please cite the following paper:

@misc{tarafdar2026interpretablefrugallearningsystems,
      title={Interpretable and Frugal Learning Systems Employing Multiresolution Pyramids and Volterra Kernels},
      author={Kishore Kumar Tarafdar},
      year={2026},
      eprint={2606.15011},
      archivePrefix={arXiv},
      primaryClass={eess.SP},
      url={https://arxiv.org/abs/2606.15011},
}

License

Apache License 2.0. See LICENSE.