PySCSA — Semi-Classical Signal Analysis

A Python library for signal and image processing based on the Semi-Classical Signal Analysis (SCSA) framework.

How It Works

SCSA treats a signal $y(x) \geq 0$ as the potential of a Schrödinger operator $\mathcal{H}_h = -h^2 d^2/dx^2 - y(x)$. Its negative eigenvalues ${-\kappa_n^2}$ and $L^2$-normalized eigenfunctions ${\psi_n}$ encode the signal's structure, and the signal is reconstructed as:

$$y_h(x) = 4h \sum_{n=1}^{N_h} \kappa_n, \psi_n^2(x)$$

The atoms $\phi_n = \psi_n^2$ are non-negative, spatially localized, and signal-adaptive — their shape is determined by $y$ itself with no fixed dictionary. The parameter $h$ controls resolution: smaller $h$ yields more atoms and finer detail; larger $h$ retains only dominant structures and suppresses noise.

C-SCSA automates the selection of $h$ by minimizing a data-driven cost balancing reconstruction fidelity against the geometric curvature of $y_h$ — a proxy for noise energy (Li & Laleg-Kirati, IET Signal Processing 2021). No knowledge of peak locations or noise level is required.

For the full mathematical treatment see the documentation and references below.

Installation

pip install pyscsa

For development:

git clone https://github.com/boost-inria/pyscsa.git
cd pyscsa
pip install -e .

Quick Start

1D Signal Denoising

from pyscsa import SCSA1D
import numpy as np

x = np.linspace(-10, 10, 500)
signal = -2 / np.cosh(x)**2
noisy = signal + 0.1 * np.random.randn(len(signal))

scsa = SCSA1D(gmma=0.5)
result = scsa.filter_with_c_scsa(noisy)

print(f"Optimal h : {result.optimal_h:.4f}")
print(f"PSNR      : {result.metrics['psnr']:.2f} dB")

2D Image Denoising

from pyscsa import SCSA2D
import numpy as np

image = np.random.rand(128, 128)
noisy = image + 0.05 * np.random.randn(*image.shape)

scsa = SCSA2D(gmma=2.0)
denoised = scsa.denoise(noisy, method='windowed', window_size=8, h=5.0)

Features

• 1D & 2D processing — reconstruction and denoising via spectral decomposition of a Schrödinger-type operator
• C-SCSA — automatic bandwidth parameter selection via curvature penalty, no peak localization required
• Windowed mode — memory-efficient processing of large images
• Performance metrics — MSE, RMSE, PSNR, SNR out of the box
• Visualization — built-in plotting utilities via SCSAVisualizer

API Reference

Full documentation: pyscsa.readthedocs.io

Testing

pytest tests/ -v
pytest tests/ --cov=pyscsa --cov-report=html  # with coverage

Citation

@software{pyscsa,
  title  = {PySCSA: Python Semi-Classical Signal Analysis Library},
  author = {A. Guir, I.J.S. Filho, J.M. Vargas and T.M. Laleg},
  year   = {2025},
  url    = {https://github.com/boost-inria/pyscsa}
}

@article{li2021cscsa,
  title   = {Signal denoising based on the Schrödinger operator's eigenspectrum and a curvature constraint},
  author  = {Li, P. and Laleg-Kirati, T.M.},
  journal = {IET Signal Processing},
  volume  = {15},
  pages   = {195--206},
  year    = {2021},
  doi     = {10.1049/sil2.12023}
}

@misc{lalegkirati2010scsa,
  title         = {Semi-classical signal analysis},
  author        = {Laleg-Kirati Taous-Meriem, Crépeau Emmanuelle and Sorine Michel},
  year          = {2010},
  eprint        = {1007.0938},
  archivePrefix = {arXiv},
  primaryClass  = {math-ph}
}

License

GNU Affero General Public License v3.0 (AGPL-3.0-only) — see LICENSE for details.