Package usage and technical notes¶
This page is a collection of usage and code related notes about the image differencing implementation. We do not summarise the Alard-Lupton (AL) [AL_1998] and Zackay, Ofek, Gal-Yam (ZOGY) [ZOGY2016] papers themselves here.
Usage notes¶
Supported input data¶
ImageDifferenceTask supports two types of data products as templates,
coadds and calexps, which can be subtracted from calexp science
exposures only. Other combinations of inputs are not supported. The
input mode is selected by the getTemplate configurable field. The
getTemplate subtask is a properly retargetable top level
pexConfig.ConfigurableField with two supported target subtasks:
GetCoaddAsTemplate and GetCalexpAsTemplate.
Enabling processing steps¶
There is a sequence of pre-subtraction and post-subtraction processing
steps included in ImageDifferenceTask around the actual
subtraction operation of the images. Including the subtraction
operation itself, these steps can be enabled or disabled by top level
do<ACTION> configuration options. These top-level configuration
options are summarised in Figure 3 and
Figure 4 (flowchart source and standalone pdf version
). Some of these top level configuration options are also passed on to
invoked subtasks and influence their functionality. They may not be
specified for the subtasks directly.
Figure 3 Top level subtasks and top level configuration options in
ImageDifferenceTask.
here.
Figure 4 Top level configuration options in ZogyTask.
Specifying a coadd as template¶
Using the GetCoaddAsTemplate subtask, we specify one or more
science exposures by the --id general data specification
option. Tract or patch specification as part of the --id option
are silently ignored. The given (coaddName, defaults to “deep”)
type coadd is looked up in the same input repository automatically.
As of Butler generation 2, if multiple coadd templates are reachable
through the repository parent references, one of them is picked
automatically.
The subtask detemines the sky corners of a box that fully contains the
science exposure with a configurable boundary
(templateBorderSize). The subtask selects all patches of the coadd
skymap that overlap with the science exposure and cuts them
accordingly to assemble the template coadd image. The template coadd
image inherits the coadd WCS. It is an error if there is no
overlapping region. The --templateId option is silently
ignored. The following example specifies one science exposure and
implicitly the deep coadd residing in the same repository for image
differencing:
imageDifference.py repo/ingested/ --id visit=410915 filter=g
ccdnum=25
GetCoaddAsTemplate also supports loading DcrModel coadds and
produce a color corrected template matching the filter of the
science exposure.
Specifying a calexp as template¶
Using the GetCalexpAsTemplate subtask, we can select two calexp
data products for subtraction. The --id option specifies a data
reference of one or more science exposures (calexp). The
--templateId specifies a data reference for the template
(calexp). Fields that are not specified for the template are inherited
from the science exposure data reference. The following example
subtract visit 410915 ccdnum 25 (template) from 411055 ccdnum 25
(science exposure):
imageDifference.py repo/calibimgs --id visit=411055
ccdnum=25 --templateId visit=410915
Implementation notes¶
General¶
If the two images have the same origin and extent (same WCS) the subtraction is performed pixel by pixel. Otherwise, the template exposure is warped and resampled into the WCS frame of the science exposure.
The AL kernel fitting is entirely implemented in C++, an adaptation of
the hotpants C package
by Becker, while the ZOGY algorithm is entirely implemented in
Pyton based on mostly on the numpy FFT functionality.
Beside the top level configuration options, the AL algorithm has its own set of separate configuration parameters, while the ZOGY algorithm does not have any algorithm specific options.
Alard-Lupton algorithm¶
The Alard-Lupton numerical fitting for the coefficients (of the composing basis kernel functions) of the image convolution kernel is performed independently on a number of stamp images around selected sources. These independent solutions are called kernel candidates throughout the code. The final kernel solution model for the whole image is a smoothly varying spatial fit of the coefficients as a function of the image pixel coordinates.
If convolveTemplate==False the science exposure is convolved and
then the template is subtracted from the science image.
The performance of the AL algorithm was studied in details in the
[Becker_LDM-227] report. This study forms the basis of the AL
algorithm default values; the degree of the polynomial
multiplicator of the Gaussian kernel basis functions (degGauss),
the degree of the polynomial that is fitted to the spatial variaton of
the solution coefficients accross the image (spatialKernelOrder)
and the default detection thresholds (5.5 sigma). As a legacy of this
study, the Winter2013ImageDifferenceTask is still available in
imageDifference.py though it is unclear which test data repository
it requires.
Due to noise in the template image, convolving the template introduces correlation in the noise in the template image. The AL algorithm was improved by an additional afterburner decorrelation to remove the noise correlation in the image difference. The implemented decorrelation method and its mathematical formulae of the decorrelation kernel is summarised and studied in [Reiss_DMTN-021].
Zackay-Ofek-Gal-Yam algorithm¶
[ZOGY2016] is free from the assumption that the template is noise free or specially selected by any other means. We simply deal with two images with different PSFs and noise characteristics (sigma). In the basic version of the algorithm, the random noise in the pixels are assumed to be background dominated i.e. uncorrelated between pixels and independent of the pixel values. Also we assume that the noise has zero expectation value i.e. the expectation value of the random noise is already removed. ZOGY shows that if these assumptions hold, the difference image noise is also independent and identically distributed over its pixels (white) by construction, there is no need to decorrelate the noise in the difference image.
Following the variance addition rule of the difference of uncorrelated random variables, exactly the same steps are repeated on the exposure variance planes as on the data planes, only the subtraction step is replaced by addition.
The nan values are removed from the science and template images
before Fourier transformations and replaced by the image mean
values. On the immage difference, the mask plane UNMASKEDNAN is
set for pixels where originally any of the two inputs or the
difference result is nan.
Pre-convolution is not implemented in the ZOGY algorithm. In case of
the ZOGY algorithm, the doPreConvolve==True config option selects
the detection likelihood image to be returned instead of the
difference image. Under the assumptions of the algorithm, this image
carries the likelihood ratio test statistic values similarly to the
usual match filter-convolved image and can be used for threshold
source detections. The S detection likelihood (or score) image
(eq. 12 in [ZOGY2016]) and its corrected variance S_var (the
denominator of eq. 25 [ZOGY2016]) are calculated and returned,
following the simple correction steps presented in the paper Section
3.3. This signal correction is introduced to account for the source
noise (bright sources) and also for other systematic noise
sources. The iterative approach of section 3.5 is not implemented.
References¶
| [AL_1998] | Alard, C.; Lupton, Robert H. A Method for Optimal Image Subtraction |
| [Reiss_DMTN-021] | Reiss J. David, Lupton, Robert H. DMTN-021: Implementation of Image Difference Decorrelation |
| [ZOGY2016] | (1, 2, 3, 4) Zackay B., Ofek E. O., Gal-Yam A., Proper Image Subtraction—Optimal Transient Detection, Photometry, and Hypothesis Testing, 2016, ApJ, 830, 27 |
| [Becker_LDM-227] | Becker A. et al. LDM-227 Report on Late Winter2013 Production: Image Differencing |