# Total variation vs L1 regularization: a comparison of compressive sensing optimization methods for chemical detection

## TL;DR

This paper compares L1 and total variation regularization methods in compressive sensing for chemical detection, demonstrating that L1 regularization generally outperforms TV in real-world datasets at high compression rates.

## Contribution

The study provides a comprehensive comparison of L1 and TV regularization in CS for chemical detection, highlighting the superiority of L1 in practical hyperspectral data scenarios.

## Key findings

- L1 regularization outperforms TV in chemical detection accuracy.
- Both methods achieve successful detection at 90% compression.
- L1 regularization results in fewer false positives in reconstructed data.

## Abstract

One of the fundamental assumptions of compressive sensing (CS) is that a signal can be reconstructed from a small number of samples by solving an optimization problem with the appropriate regularization term. Two standard regularization terms are the L1 norm and the total variation (TV) norm. We present a comparison of CS reconstruction results based on these two approaches in the context of chemical detection, and we demonstrate that optimization based on the L1 norm outperforms optimization based on the TV norm. Our comparison is driven by CS sampling, reconstruction, and chemical detection in two real-world datasets: the Physical Sciences Inc. Fabry-P\'{e}rot interferometer sensor multispectral dataset and the Johns Hopkins Applied Physics Lab FTIR-based longwave infrared sensor hyperspectral dataset. Both datasets contain the release of a chemical simulant such as glacial acetic acid, triethyl phosphate, and sulfur hexafluoride. For chemical detection we use the adaptive coherence estimator (ACE) and bulk coherence, and we propose algorithmic ACE thresholds to define the presence or absence of a chemical of interest in both un-compressed data cubes and reconstructed data cubes. The un-compressed data cubes provide an approximate ground truth. We demonstrate that optimization based on either the L1 norm or TV norm results in successful chemical detection at a compression rate of 90%, but we show that L1 optimization is preferable. We present quantitative comparisons of chemical detection on reconstructions from the two methods, with an emphasis on the number of pixels with an ACE value above the threshold.