# Direct Exoplanet Detection Using L1 Norm Low-Rank Approximation

**Authors:** Hazan Daglayan, Simon Vary, Valentin Leplat, Nicolas Gillis, P. -A. Absil  
**arXiv:** [2304.03619](https://arxiv.org/abs/2304.03619)  
**Date:** 2023-04-07  
**Summary page:** https://www.summarizepaper.com/en/paper/2304.03619v1/

## Key points

- Researchers propose a novel approach for imaging exoplanets using low-rank matrix approximation with the component-wise L1-norm
- Study focuses on true positives before encountering true negatives in ROC curve analysis
- Results show L2L1 performs best in cases with small separations injected, while L1L1 outperforms in instances with large separations
- Significant brightness difference between host stars and exoplanets poses challenges for detection
- Small angular distance and similarity of speckles to exoplanet signals further complicate the process
- Empirical investigation of statistical noise assumptions and evaluation of proposed L1 low-rank approximation algorithm through visual comparisons and ROC curves
- Comparison of different approaches for low-rank matrix approximation using truncated SVD based on both L1 and L2 norms in two annuli close to the star and farther away
- Utilizing L1-LRA instead of PCA for exoplanet detection can be beneficial depending on planet's distance from its host star
- Future studies may explore alternative initializations for norm approximations or develop more efficient algorithms incorporating smoothing techniques

## Summary

In the study "Direct Exoplanet Detection Using L1 Norm Low-Rank Approximation," researchers Hazan Daglayan, Simon Vary, Valentin Leplat, Nicolas Gillis, and P. -A. Absil propose a novel approach for imaging exoplanets using low-rank matrix approximation with the component-wise L1-norm. The study focuses on true positives before encountering true negatives in ROC curve analysis. Results show that in cases where a small separation is injected, L2L1 performs best in two out of three scenarios (r = {9, 17), while in instances with large separations injected, L1L1 outperforms all other methods. The significant brightness difference between host stars and exoplanets poses challenges for exoplanet detection. Additionally, the small angular distance between them and the similarity of speckles to exoplanet signals further complicates the process. To address these challenges, the researchers empirically investigate the statistical noise assumptions of their models and evaluate the performance of their proposed L1 low-rank approximation (L1-LRA) algorithm through visual comparisons and receiver operating characteristic (ROC) curves. To compare different approaches for low-rank matrix approximation in exoplanet detection, the researchers use truncated singular value decomposition (SVD) based on both L1 and L2 norms in two different annuli—one close to the star and one farther away. Further analysis involves comparing different combinations of norms (L1L1,L1L2,L2L1,L2L2) using ROC curves for various rank values (r = {9, 13, 17}). In conclusion, depending on the planet's distance from its host star,<DateTime> utilizing L1-LRA instead of principal component analysis (PCA) for exoplanet detection proves beneficial. The researchers suggest examining residual cubes obtained after applying PCA or L1-LRA to determine which method fits better for optimal low-rank matrix approximation. Future studies may explore alternative initializations for norm approximations or develop more efficient algorithms incorporating smoothing techniques. Additionally, upgrading PCA-based methods with L1-LRA could lead to improved performance outcomes over time.