Sparselandtools

Sparselandtools is a Python 3 package that provides implementations for sparse representations and dictionary learning. In particular, it includes implementations for

For Sparse Representations:

• Matching Pursuit
• Orthogonal Matching Pursuit
• Thresholding Pursuit
• Basis Pursuit

For Dictionaries in General:

• Mutual Coherence
• DCT Dictionary
• Haar Dictionary
• Overcomplete DCT Dictionary
• Visualization Tools for Dictionaries

For Dictionary Learning:

• K-SVD Algorithm
• Approximate K-SVD Algorithm

For Application:

• Approximate K-SVD Image Denoiser

Note: I did this project mainly to generate plots for my Master's thesis. Some of the implementations are more educational than efficient. If you want to learn more about sparse representations and dictionary learning using Python, or use dictionary learning algorithms in small dimensions, this package is for you. If you want to use these functions for industrial applications, you should have a look at more efficient C++-based implementations:

• The Efficient K-SVD Algorithm by Rubinstein
• The Efficient K-SVD Denoiser by Lebrun

Warning: I'm currently pursuing my PhD in computer vision and have no time to keep this project up-to-date. Any pull requests for new features or bug fixes are welcome!

Getting Started

Sparselandtools is available as a PyPI package. You can install it using

pip install sparselandtools

The following code creates a redundant (=overcomplete) DCT-II dictionary and plots it. It also prints out the dictionaries mutual coherence.

from sparselandtools.dictionaries import DCTDictionary
import matplotlib.pyplot as plt

# create dictionary
dct_dictionary = DCTDictionary(8, 11)

# plot dictionary
plt.imshow(dct_dictionary.to_img())
plt.show()

# print mutual coherence
print(dct_dictionary.mutual_coherence())

More examples can be found in the corresponding Jupyter Notebook.

Reference

If you find my implementations useful for your academic projects, feel free to cite

@software{fabian_herzog_2021_4916395,
  author       = {Fabian Herzog},
  title        = {{sparselandtools: A Python package for sparse 
                   representations and dictionary learning, including
                   matching pursuit, K-SVD and applications.}},
  month        = jun,
  year         = 2021,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.4916395},
  url          = {https://doi.org/10.5281/zenodo.4916395}
}