TFAW: Wavelet-based signal reconstruction to reduce photometric noise in time-domain surveys

Abstract

Context. There have been many efforts to correct systematic effects in astronomical light curves to improve the detection and characterization of planetary transits and astrophysical variability. Algorithms like the Trend Filtering Algorithm (TFA) use simultaneouslyobserved stars to measure and remove systematic effects, and binning is used to reduce high-frequency random noise. Aims. We present TFAW, a wavelet-based modified version of TFA. TFAW aims first, to increase the periodic signal detection and second, to return a detrended and de-noised signal without modifying its intrinsic characteristics. Methods. We modify TFA's frequency analysis step adding a Stationary Wavelet Transform filter to perform an initial noise and outlier removal and increase the detection of variable signals. A wavelet-based filter is added to TFA's signal reconstruction to perform an adaptive characterization of the noise-and trend-free signal and the underlying noise contribution at each iteration while preserving astrophysical signals. We carried out tests over simulated sinusoidal and transit-like signals to assess the effectiveness of the method and applied TFAW to real light curves from TFRM. We also studied TFAW's application to simulated multiperiodic signals.Results. TFAW improves the signal detection rate by increasing the signal detection efficiency (SDE) up to a factor ∼2.5× for low SNR light curves. For simulated transits, the transit detection rate improves by a factor ∼2-5× in the low-SNR regime compared to TFA. TFAW signal approximation performs up to a factor ∼2× better than bin averaging for planetary transits. The standard deviations of simulated and real TFAW light curves are ∼40% better compared to TFA. TFAW yields better MCMC posterior distributions and returns lower uncertainties, less biased transit parameters and narrower ( ∼10×) credibility intervals for simulated transits. TFAW is also able to improve the characterization of multiperiodic signals. We present a newly-discovered variable star from TFRM.

Precise Photometric Transit Follow-up Observations of Five Close-in Exoplanets: Update on Their Physical Properties

“…The light curves were denoised using wavelet denoising technique before modeling to decorrelate the patterns of variability common to all the stars in the frame but uncorrelated in time (del Ser et al 2018). Also, to take care of the noise pattern unique to the host stars and correlated in time caused by stellar activity or pulsation etc.,we have adopted Gaussian process correlated noise modeling technique during modeling to model its covariance structure and to take it into account when calculating the likelihood of the data given the model (Johnson et al 2015;Barclay et al 2015).…”

“…Wavelets have already been used extensively in the light curve noise analysis and filtering (Cubillos et al 2017;Waldmann 2014). In case of transit photometry, wavelet denoising can efficiently remove the outliers, yield better MCMC posterior distributions and reduce the bias in the fitted transit parameters and their uncertainties (del Ser et al 2018). We used the pywt package (Lee et al 2018) and followed the same procedure as described in del Ser et al (2018).…”

“…Wavelet-based light curve noise analysis and filtering can be found in Cubillos et al (2017); Waldmann (2014). In case of transit photometry, del Ser et al (2018) has shown that this denoising technique does not alter the underlying astrophysical signals but improves the results obtained after modeling the transit light curves. Such preprocessing of data is a part of our self-developed pipeline used for reduction, analysis and modeling.…”

Multi-band transit follow up observations of five hot-Jupiters with critical noise treatments: Improved physical properties

“…Hence, instead of smoothing the light curves with some low-pass filter, we used a more robust technique, namely the Wavelet Denoising (Donoho & Johnstone 1994;Quan Pan et al 1999;Luo & Zhang 2012). Although wavelet based denoising techniques have been widely used in image processing and remote sensing in various fields of science and engineering, it is a recent addition in the context of transit photometry and other light curve analysis (e.g., del Ser et al 2018;Cubillos et al 2017;Waldmann 2014). CS19 applied this technique on the light curves obtained from their observational data and demonstrated that this technique produces no distortion in the transit light curves, but yields better MCMC posterior distributions for the fitted transit parameters.…”

“…Most of the pre-processing techniques (such as binning and Gaussian smoothing) that can reduce the effect of these timeuncorrelated noise components also tend to distort the shape of the transit signal. CS19 have demonstrated that the Wavelet Denoising technique (Donoho & Johnstone 1994;Quan Pan et al 1999;Luo & Zhang 2012;del Ser et al 2018;Cubillos et al 2017;Waldmann 2014) can be used to reduce the time-uncorrelated fluctuations in the light-curves without distorting the transit signal and improves the precision of the estimated physical parameters (see Table 3 and Table 4 of CS19) to a great extent. Wavelet denoising technique also reduces the outliers in the light-curves due to cosmic ray events.…”