L1TV

May 11, 2026 · View on GitHub

PyPI Python License: MIT CI MATLAB

Exact, non-iterative L1-TV regularisation for noisy 1D signals — for both real-valued and circle-valued (phase / orientation) data.

L1 TV denoising of a real-valued signal

Paper

M. Storath, A. Weinmann, M. Unser. Exact algorithms for L¹-TV regularization of real-valued or circle-valued signals. SIAM Journal on Scientific Computing, 38(1), A614–A630, 2016.

Quickstart

Python (Rust core)

pip install l1tv

import numpy as np
from l1tv import min_l1_tv

# noisy real-valued signal
y = np.array([0.0, 0.1, -0.05, 1.05, 0.95, 1.1])
x = min_l1_tv(y, alpha=0.5)

The Python package wraps a Rust extension built with PyO3 and maturin; algorithm crate lives under src/, demos under demos_python/. See README_PYTHON.md for the full Python API, including the circle-valued variant min_l1_tv_circ.

MATLAB

The original MATLAB reference implementation is in this same repository:

  1. Set the MATLAB path by running setPath.m.
  2. Run a demo from the Demos/ folder.

Application examples

The hero image above shows the real-valued case. The circle-valued variant handles phase / orientation data with wrap-around, without any unwrapping pre-step:

L1 TV denoising of circle-valued signal

How to cite

If you use this software, please cite the paper above. GitHub's "Cite this repository" button on the repo page reads the version and date-released fields from CITATION.cff and renders BibTeX/APA.

See also

Sibling projects from the same research program on variational methods for signal and image processing:

  • Pottslab — multilabel image segmentation via the Potts / piecewise-constant Mumford-Shah model
  • CSSD — cubic smoothing splines for signals with discontinuities
  • MumfordShah2D — edge-preserving image restoration via the Mumford-Shah model
  • CircleMedianFilter — fast median filtering for phase or orientation data
  • DCEBE — bolus arrival time estimation for DCE-MRI signals

License

Released under the MIT License. See LICENSE.

Project history

The Python / Rust port of this codebase was generated from the original MATLAB reference by a Claude coding agent in 2026. See PORTED_BY.md for full attribution and the porting plan.