A Python package for sparse representations and dictionary learning, including matching pursuit, K-SVD and applications.
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PyPI - Python Version PyPI PyPI - Implementation Build Status

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:

Getting Started

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

pip install sparselandtools

DCT and Haar Dictionary

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

# print mutual coherence

More examples can be found in the corresponding Jupyter Notebook.


There are a lot of algorithms based on sparse representations and dictionary learning that are not (yet) included in this package. These include - among others:

  • The Double Sparsity Method
  • Trainlets
  • Denoiser with Method Noise Post Processing
  • Boosted Denoiser with Patch Disagreement

and much more. It would also be interesting to see more applications in this package. Currently, this package only provides the K-SVD image denoiser based on the work of Aharon and Elad. K-SVD can also be used in many other applications, such as face recognition. Furthermore, it would be nice to have GPU-versions of all the algorithms available as well.

If you want to see a specific algorithm in this package, please consider opening a feature request here on Github. If you have written an algorithm that you think would fit into this package, please fork this repository, add your algorithm and file a pull request. If something doesn't work as expected, please open an issue.