ANNOUNCEMENT: This package has been integrated in scikit-ued. Improvements made in scikit-ued's baseline subpackage will not be backported to dualtree

dualtree

Python package, based on PyWavelets, implementing Nick Kingsbury's dual-tree complex wavelet transform.

The purpose of implementing the dual-tree complex wavelet transform was for it's use in baseline-removal of digital signals. This package is provided as part of the research published in the following article:

L. P. René de Cotret and B. J. Siwick, A general method for baseline-removal in ultrafast electron powder diffraction data using the dual-tree complex wavelet transform, Struct. Dyn. 4 (2017) DOI: 10.1063/1.4972518.

From the package docstrings:

dualtree, idualtree

Dual-tree complex wavelet transform (and its inverse) implemented using PyWavelets. Implementation tricks from [1], such as first stage filtering and filter swapping at later stages, are also included.

approx_rec, detail_rec

Decomposition and recomposition of signals using only approximate or detail coefficients.

dualtree_max_level

Maximal decomposition level of the dual-tree complex wavelet transform.

baseline

Baseline determination of signals using the dual-tree complex wavelet transform. Modified algorithm from [2].

denoiseDenoising of signals using the dual-tree complex wavelet transform.

dualtree_wavelet

Pair of real and imaginary wavelet that forms a complex wavelet appropriate for the dual-tree complex wavelet transform.

dualtree_first_stage

Pair of real and imaginary wavelet, shifted by one sample with respect to one another, forming a complex wavelet appropriate for first-stage filtering during the dual-tree complex wavelet transform.

Example

We start with the base:

>>> from dualtree import dualtre, idualtree, baseline
>>> import matplotlib.pyplot as plt

Here is an example of getting the dual-tree complex wavelet transform coefficients from real data:

>>> signal = n.load('~\data\diffraction.npy')                           # Included example electron diffraction data
>>> coeffs = dualtree(signal, wavelet = 'qshift3', level = 4)
>>> reconstructed = idualtree(coeffs = coeffs, wavelet = 'qshift3')     # level is inferred
>>> n.allclose(signal, reconstructed)                                   # Check perfect reconstruction
True

Example of algorithm (baseline-determination) on a NumPy array:

>>> signal = n.load('~\data\diffraction.npy')
>>> background = baseline(signal, wavelet = 'qshift3', max_iter = 100)  # Might not be optimal parameters
>>> plt.plot(signal, '.k', background, '.r')

References

Selesnick, I. W. et al. The Dual-tree Complex Wavelet Transform, IEEE Signal Processing Magazine pp. 123 - 151, November 2005.
Galloway et al. An Iterative Algorithm for Background Removal in Spectroscopy by Wavelet Transforms, Applied Spectroscopy pp. 1370 - 1376, September 2009.

LaurentRDC / dualtree