Spectroscopy from Photometry Using Sparsity. The SDSS Case Study

TL;DR

This paper demonstrates that medium-resolution stellar spectra can be effectively reconstructed from limited photometric data using sparsity-based methods, enabling spectroscopic analysis from broad-band photometry.

Contribution

It introduces a novel sparsity-constrained least-squares approach to reconstruct spectra from photometry, validated with SDSS data, achieving high accuracy with minimal filters.

Findings

Reconstruction with three principal components yields spectra within 5% of original.

High photometric precision results in very small reconstruction errors.

Method enables spectroscopic analysis from photometric data for large stellar samples.

Abstract

We explore whether medium-resolution stellar spectra can be reconstructed from photometric observations, taking advantage of the highly compressible nature of the spectra. We formulate the spectral reconstruction as a least-squares problem with a sparsity constraint. In our test case using data from the Sloan Digital Sky Survey, only three broad-band filters are used as input. We demonstrate that reconstruction using three principal components is feasible with these filters, leading to differences with respect to the original spectrum smaller than 5%. We analyze the effect of uncertainties in the observed magnitudes and find that the available high photometric precision induces very small errors in the reconstruction. This process may facilitate the extraction of purely spectroscopic quantities, such as the overall metallicity, for hundreds of millions of stars for which only photometric information is available, using standard techniques applied to the reconstructed spectra.