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Title: Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra

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 provide excellent filtering for 1D stellar spectra, at a low computational cost. 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. Finally, 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,more » LEGA-C, and DESI.« less

Authors:
 [1];  [2]
  1. Univ. of Florida, Gainesville, FL (United States)
  2. Univ. of Florida, Gainesville, FL (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1603546
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Monthly Notices of the Royal Astronomical Society
Additional Journal Information:
Journal Volume: 490; Journal Issue: 4; Journal ID: ISSN 0035-8711
Publisher:
Royal Astronomical Society
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; data analysis; statistical; image processing; spectroscopic

Citation Formats

Gilda, Sankalp, and Slepian, Zachary. Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra. United States: N. p., 2019. Web. https://doi.org/10.1093/mnras/stz2577.
Gilda, Sankalp, & Slepian, Zachary. Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra. United States. https://doi.org/10.1093/mnras/stz2577
Gilda, Sankalp, and Slepian, Zachary. Mon . "Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra". United States. https://doi.org/10.1093/mnras/stz2577. https://www.osti.gov/servlets/purl/1603546.
@article{osti_1603546,
title = {Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra},
author = {Gilda, Sankalp and Slepian, Zachary},
abstractNote = {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 provide excellent filtering for 1D stellar spectra, at a low computational cost. 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. Finally, 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.},
doi = {10.1093/mnras/stz2577},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 4,
volume = 490,
place = {United States},
year = {2019},
month = {9}
}

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