l1tv 1.0.0

Exact L1-TV regularisation of real- or circle-valued 1-D signals — Python/Rust port of MATLAB l1tv (Storath, Weinmann, Unser 2016)

l1tv

Exact L1-TV regularisation of real-valued or circle-valued 1-D signals — a Python/Rust port of the original MATLAB L1TV by Martin Storath and Andreas Weinmann.

What it does

Solves the L1 total-variation problem in one dimension to global optimum:

• Real-valued —

  argmin_x  α · ∑ |x[i] - x[i+1]|  +  ∑ w[i] · |x[i] - y[i]|
  

• Circle-valued (phase / orientation data) —

  argmin_x  α · ∑ d_arc(x[i], x[i+1])  +  ∑ w[i] · d_arc(x[i], y[i])
  

  where d_arc is the shortest-arc distance on the unit circle.

Unlike iterative TV solvers (PDHG, ADMM, FISTA), the algorithm is exact and non-iterative — it returns a global minimiser in O(N · K) time, where K = |unique(y)|, via dynamic programming on the candidate set plus an L1 distance transform speedup.

Why use it

• Exactness. No tolerance/maxiter knobs — the returned x is a global optimum to floating-point precision.
• Robustness. L1 data fidelity tolerates impulse / heavy-tail noise that derails L2 methods.
• Phase data. The circular variant handles wrap-around without needing unwrapping, useful for phase-unwrapping / orientation-field denoising.

Installation

From PyPI (once published):

pip install l1tv

From source (Rust toolchain required):

git clone https://github.com/mstorath/L1TV
cd L1TV
pip install maturin
maturin develop --release

Optional test/dev dependencies:

pip install l1tv[test]   # adds scipy + pytest + matplotlib

Quick start

import numpy as np
import l1tv

# --- real-valued: piecewise-constant denoising ---
rng = np.random.default_rng(0)
y = np.repeat(rng.standard_normal(20), 50) + 0.3 * rng.standard_normal(1000)
x = l1tv.min_l1_tv(y, alpha=0.5)            # exact L1-TV solution

# --- circle-valued: phase denoising ---
phase = np.repeat(rng.uniform(-np.pi, np.pi, 20), 50)
y_phase = (phase + 0.3 * rng.standard_normal(1000) + np.pi) % (2*np.pi) - np.pi
x_phase = l1tv.min_l1_tv_circ(y_phase, alpha=0.5)

Per-sample data weights:

weights = np.where(np.isnan(y), 0.0, 1.0)   # zero-weight masked samples
x = l1tv.min_l1_tv(np.nan_to_num(y), alpha=0.5, weights=weights)

Reference

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. https://doi.org/10.1137/15M101796X

If you use this package in academic work, please cite both the paper above and the package via CITATION.cff (GitHub renders a "Cite this repository" button on the repo page).

Provenance and license

This Python/Rust package is an automated port of the original MATLAB implementation by Storath and Weinmann, performed by Claude Opus coding agent (Anthropic, 2026). See PORTED_BY.md for the file-by-file mapping. Algorithmic semantics are preserved — only input handling, memory layout, and tooling surface changed. License: MIT (unchanged from the original).

Related packages in the same research family

• pottslab — Potts / piecewise-constant Mumford-Shah segmentation (1-D and 2-D, L1 and L2).
• pycirclemedianfilter — fast median filter for circle-valued data.
• CSSD — cubic smoothing splines with discontinuities.

These packages all originate from the Lab for Mathematical Methods in Computer Vision and Machine Learning, THWS.