lightkurve.correctors.
PLDCorrector
(tpf)¶Bases: object
Implements the Pixel Level Decorrelation (PLD) systematics removal method.
Pixel Level Decorrelation (PLD) was developed by [1] to remove systematic noise caused by spacecraft jitter for the Spitzer Space Telescope. It was adapted to K2 data by [2] and [3] for the EVEREST pipeline [4].
For a detailed description and implementation of PLD, please refer to these references. Lightkurve provides a reference implementation of PLD that is less sophisticated than EVEREST, but is suitable for quicklook analyses and detrending experiments.
Our simple implementation of PLD is performed by first calculating the noise model for each cadence in time. This function goes up to second order, and is represented by
\[m_i = \sum_l a_l \frac{f_{il}}{\sum_k f_{ik}} + \sum_l \sum_m b_{lm} \frac{f_{il}f_{im}}{\left( \sum_k f_{ik} \right)^2} + \alpha + \beta t_i + \gamma t_i^2\]where
 \(m_i\) is the noise model at time \(t_i\)
 \(f_{il}\) is the flux in the \(l^\text{th}\) pixel at time \(t_i\)
 \(a_l\) is the firstorder PLD coefficient on the linear term
 \(b_{lm}\) is the secondorder PLD coefficient on the \(l^\text{th}\), \(m^\text{th}\) pixel pair
 \(\alpha\), \(\beta\), and \(\gamma\) are the Gaussian Process terms applied to capture longperiod variability.
We perform Principal Component Analysis (PCA) to reduce the number of vectors in our final model to limit the set to best capture instrumental noise. With a PCAreduced set of vectors, we can construct a design matrix containing first and second order fractional pixel fluxes.
To solve for the PLD model, we need to minimize the difference squared
\[\chi^2 = \sum_i \frac{(y_i  m_i)^2}{\sigma_i^2},\]where \(y_i\) is the observed flux value at time \(t_i\), by solving
\[\frac{\partial \chi^2}{\partial a_l} = 0.\]
References
[1]  (1, 2) Deming et al. (2015), ads:2015ApJ…805..132D. (arXiv:1411.7404) 
[2]  (1, 2) Luger et al. (2016), ads:2016AJ….152..100L (arXiv:1607.00524) 
[3]  (1, 2) Luger et al. (2018), ads:2018AJ….156…99L (arXiv:1702.05488) 
[4]  (1, 2) EVEREST pipeline webpage, https://rodluger.github.io/everest 
Examples
Download the pixel data for GJ 9827 and obtain a PLDcorrected light curve:
>>> import lightkurve as lk
>>> tpf = lk.search_targetpixelfile("GJ9827").download() # doctest: +SKIP
>>> corrector = lk.PLDCorrector(tpf) # doctest: +SKIP
>>> lc = corrector.correct() # doctest: +SKIP
>>> lc.plot() # doctest: +SKIP
However, the above example will overfit the small transits!
It is necessary to mask the transits using corrector.correct(cadence_mask=...)
.
Methods Summary
correct ([aperture_mask, cadence_mask, …]) 
Returns a PLD systematicscorrected LightCurve. 
Methods Documentation
correct
(aperture_mask=None, cadence_mask=None, gp_timescale=30, n_components_first=None, n_components_second=20, use_gp=True)¶Returns a PLD systematicscorrected LightCurve.
Parameters: 


Returns: 

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