LORABEL

Thermal Background Reduction for Mid-Infrared Imaging by Low-Rank Background and Sparse Point Source Modelling

LORABEL implements LOw-RAnk Background ELimination, a novel computational method to improve sensitivity in mid-infrared astronomical imaging by modelling and removing varying thermal background noise without classical chopping or nodding.

---

Table of Contents

1. Features
2. Installation
3. Quick Start
4. Algorithm Overview
5. Parameters & Tuning
6. Citation
7. License
8. Authors & Acknowledgements

---

Features

• Low-Rank Background Modelling: captures quasi-static and slowly varying background patterns

• Sparse Point Source Extraction: isolates astrophysical point sources via ℓ₁ regularization

• Stable Principal Component Pursuit: solves

  minimize ‖B‖_* + θ‖C‖₁
  s.t. ‖A - B - C‖_F ≤ δ
  

• No Nodding Required: works on chop-only data, reducing operational overhead

• Flexible: demonstrated on ground-based VISIR and airborne SOFIA/FORCAST datasets

Installation

Install directly from GitHub:

pip install git+https://github.com/vandeplaslab/lorabel.git

---

Quick Start

from astropy.io import fits
from lorabel import LORABEL

# Load your chop subtraction time series: a 3D array (height × width x frames) and reshape to 2D array (pixels x frames)
hdul = fits.open('chop_series.fits')
data = hdul[0].data  # shape (height, width, frames)
hdul.close()
data = data.reshape(data.shape[0], -1)

# Initialize the model (θ and δ can be adjusted)
model = LORABEL()

# Decompose into low-rank background, sparse sources, and residual noise
background, sources, residual = model.decompose(data)

# Aggregate the sparse component to detect and photometer point sources
time_avg = sources.mean(axis=0)
# ... proceed with your favorite photometry routine

---

Algorithm Overview

1. Vectorize Frames: build matrix $A\in\mathbb{R}^{mn \times t}$ with each column as a vectorized chop subtraction frame.

2. Model: $A = B + C + D$ where:

   • $B$ is low-rank (background)
   • $C$ is sparse (point sources)
   • $D$ is small dense noise

3. Optimization: solve Stable Principal Component Pursuit:

   minimize ‖B‖_* + θ‖C‖₁
   subject to ‖A - B - C‖_F ≤ δ
   

4. Reconstruct: reshape $B,C,D$ back to 3D cubes for further analysis.

---

Parameters & Tuning

• θ (theta): trade-off between sparsity and background rank. Default ≈ 1/√max(m,n).
• δ (delta): noise tolerance, often estimated as √(mn)·σ (σ = noise σ).

Supply custom values:

model = LORABEL(data, theta=1.1/np.sqrt(max(m, n)), delta=0.7*np.linalg.norm(A, 'fro'))

---

Citation

If you use LORABEL in your research, please cite (submitted to A&A):

R.A.R. Moens, A.G.M. Pietrow, B. Brandl, & R. Van de Plas (2025), “Thermal Background Reduction for Mid-Infrared Imaging by Low-Rank Background and Sparse Point Source Modelling,” * *, DOI: xx.xxxx/XXXX

---

License

This project is licensed under the BSD 3-Clause License. See LICENSE for details.

---

Authors & Acknowledgements

Authors: R.A.R. Moens, A.G.M. Pietrow, B. Brandl, R. Van de Plas

This package leverages open-source tools: NumPy, Matplotlib, Astropy, Photutils.

Supported by: TU Delft Space Institute, DFG, ESO, NASA/SOFIA.

Contributions and issues are welcome on GitHub.