powersmooth 0.1.1

Derivative-based regularization smoothing for 1D signals on uniform and non-uniform grids

powersmooth

Python implementation of powersmooth (https://de.mathworks.com/matlabcentral/fileexchange/48799-powersmooth), invented by B. M. Friedrich.

This package provides derivative-based regularization smoothing for one-dimensional signals on uniform and non-uniform grids.

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Mathematical Formulation

Given data points $ (x_i, y_i) $, the smoothed signal $ u $ is computed as the minimizer of

$$ \min_u ; | M (u - y) |2^2 ;+; \sum{k} w_k | D_k u |_2^2 $$

where:

• $ M $ is a diagonal mask matrix controlling data fidelity
• $ D_k $ is a finite-difference approximation of the $ k $-th derivative
• $ w_k \ge 0 $ are regularization weights

This allows explicit penalization of first, second, or third derivatives.

The method works on:

• Non-uniform grids
• Uniform grids
• Upsampled grids with masked original data points

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Installation

From PyPI

pip install powersmooth

From GitHub

git clone https://github.com/Coolix99/powersmooth.git
cd powersmooth
pip install .

For development (editable install):

pip install -e .

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Quick Example

import numpy as np
from powersmooth import powersmooth_general

# Generate noisy data
x = np.linspace(0, 10, 50)
y = np.sin(x) + 0.3 * np.random.randn(len(x))

# Penalize second derivative (curvature)
weights = {2: 1e-2}

y_smooth = powersmooth_general(x, y, weights)

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Requirements

• Python ≥ 3.9
• NumPy
• SciPy

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License

MIT License