# Automatic Kalman-Filter-based Wavelet Shrinkage Denoising of 1D Stellar Spectra

## TL;DR

This paper introduces an adaptive Kalman-filter-based wavelet denoising method for 1D stellar spectra that improves noise reduction and peak preservation without requiring parameter tuning, outperforming traditional methods.

## Contribution

It presents a novel adaptive Kalman thresholding approach combined with wavelet shrinkage, eliminating the need for choosing decomposition levels in denoising stellar spectra.

## Key findings

- Superior noise suppression compared to common methods
- Better peak shape preservation in denoised spectra
- Effective for synthetic and potentially real survey data

## Abstract

We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the Discrete Wavelet Transform (DWT) to the input signal, `shrinking' certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by `trial and error', which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the `Haar' wavelet basis, which we found to be the best-suited for 1D stellar spectra. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. We expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI.