The Numerical Tours, by Gabriel Peyré and contributors, connect mathematical methods with experiments in imaging, machine learning, computer vision, and geometry. Topics include optimization, partial differential equations, optimal transport, inverse problems, and sparse representations.
The main Python collection consists of Jupyter notebooks with explanations, complete implementations, figures, and further reading. Read a tour on the website or open it in Colab to experiment. The MATLAB, Julia, and R collections remain available separately.
How to use a tour
Read the introduction, run the setup, and follow the cells in order. Each worked example shows its solution directly. Modify the data or parameters to test your understanding, and use the references at the end to explore the theory in more depth. See Getting started for local installation instructions.
The course slides and companion notes develop the underlying mathematical ideas.
Cite the Numerical Tours
If you use these experiments in research or teaching, please cite:
Gabriel Peyré. The Numerical Tours of Signal Processing—Advanced Computational Signal and Image Processing. Computing in Science & Engineering, 13(4), 94–97, 2011.
Please also cite the relevant original methods listed in each tour’s bibliography.
Contribute
The notebooks and website are maintained in the Numerical Tours repository. Contributions that improve mathematical explanations, numerical reliability, accessibility, or reproducibility are welcome. Include an end-to-end execution when changing a Python tour.
For a complementary collection of mathematical essays, visit the Mathematical Tours.