Overview

Curvelets is an open-source implementation of the Uniform Discrete Curvelet Transform (UDCT) [Nguyen and Chauris, 2010] in the Python programming language for N-dimensional signals.

Getting Started

Installation

Curvelets can be installed directly from the PyPI index:

pip install curvelets

or, if you want to use the PyTorch backend, you can install the torch optional dependency:

pip install curvelets[torch]

Curvelets supports Python 3.9 and above, NumPy 1.20 and above.

First Steps

Curvelets provides a very simple interface to use the UDCT, UDCT. Its only required argument is the shape of the inputs, but you can also supply the number of “scale” or “resolutions” (num_scales) as well as the number of wedges per direction (wedges_per_direction). The more scales there are, the more granular the distinction between a slowly-varying and a highly-varying feature. The more wedges there are, the more granular the distinction between the directions of the features. Explore the Asymmetric Directional Resolution example to better understand the effect of the scales and the wedges on the decomposition.

import numpy as np
from curvelets.numpy import UDCT

x = np.ones((128, 128))
C = UDCT(shape=x.shape)
y = C.forward(x)
np.testing.assert_allclose(x, C.backward(y))

Features

Feature	Status
N-D	✅
Arbitrary input shapes	✅
Real inputs	✅ [1]
Complex inputs	✅
Asymmetric diretionality	✅ [2]
Wavelet at highest scale	✅ [3]
Monogenic coefficients	✅ [4]
PyTorch bindings	✅ [5]

[1]

Supports real inputs with reduced storage requirements which exploit the symmetry of the real-valued Fourier transform.

[2]

The directional resolution is asymmetric in the sense that the number of wedges per direction is different for each direction. See Asymmetric Directional Resolution for an example.

[3]

Isotropic wavelets are supported. See Wavelet Transforms at the Highest Scale for an example.

[4]

The monogenic curvelet transform was originally defined for 2D signals by Storath [2010], but this implementation extends it to arbitrary N-D signals by using all Riesz transform components (one per dimension).

[5]

PyTorch bindings are supported. See PyTorch UDCT Module for an example. UDCTModule does not support the monogenic mode yet.

Credits

The original MATLAB implementation was developed by one of the authors of the UDCT, Truong T. Nguyen. The Python implementation was developed by Carlos Alberto da Costa Filho and Duy Nguyen.

References

[NC10]

Truong T. Nguyen and Hervé Chauris. Uniform Discrete Curvelet Transform. IEEE Transactions on Signal Processing, 58(7):3618–3634, jul 2010. doi:10.1109/TSP.2010.2047666.

[Sto10]

Martin Storath. The monogenic curvelet transform. In 2010 IEEE International Conference on Image Processing, 353–356. IEEE, sep 2010. doi:10.1109/ICIP.2010.5651318.