TFDST: Fast Discrete Shearlet Transform Layers in TensorFlow

TFDST provides differentiable TensorFlow/Keras layers for fast 2D and 3D discrete shearlet transforms and their inverse transforms.

Capabilities

• DST2D / IDST2D through transform=None or transform="inverse"
• DST3D / IDST3D through transform=None or transform="inverse"
• Batched multichannel TensorFlow tensors
• Backpropagation through the transform layers

Limitations

• Inputs are expected to match the configured spatial size N.
• 2D input shape: [batch, N, N, channels].
• 3D input shape: [batch, N, N, N, channels].
• Wavelet filter coefficients are provided through PyWavelets.

Installation

pip install TFDST

Minimal Example

import tensorflow as tf
from TFDST.DST2DFB import DST2D
from TFDST.DST3DFB import DST3D

N = 32

# 2D
x2 = tf.random.normal([1, N, N, 1])
dst2 = DST2D(N=N, J=2, L=[1, 2], B=[4, 8], norm=True, wave="bior1.5")
idst2 = DST2D(N=N, J=2, L=[1, 2], B=[4, 8], norm=True, wave="bior1.5", transform="inverse")
y2 = dst2(x2)
r2 = idst2(y2)

# 3D
x3 = tf.random.normal([1, N, N, N, 1])
dst3 = DST3D(N=N, J=2, L=[1, 2], B=[4, 8], norm=True, wave="bior1.5")
idst3 = DST3D(N=N, J=2, L=[1, 2], B=[4, 8], norm=True, wave="bior1.5", transform="inverse")
y3 = dst3(x3)
r3 = idst3(y3)

print(x2.shape, r2.shape)
print(x3.shape, r3.shape)

Arguments

Argument	Meaning
N	Spatial size of each axis; 2D uses N x N, 3D uses N x N x N.
J	Number of multiscale shearlet levels.
L	Shear parameters per level; must have length J.
B	Bandwidth/window parameters per level; must have length J.
wave	PyWavelets wavelet name used for the radial wavelet filters, e.g. "bior1.5".
norm	If True, applies filter-bank normalization.
transform	Use None for forward DST and "inverse" for inverse DST.

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.

Credit

1. Vineet Ghule: Basic shearlet filter-bank construction with perfect reconstruction.
2. Kishore Kumar Tarafdar: Realization as TensorFlow/Keras layers with batched multichannel I/O with biothogonal wavelet support and performance-oriented updates.

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TFDST (C) 2025 Vineet Ghule and Kishore Kumar Tarafdar, भारत 🇮🇳