Depends On: Mosaic CoAdder (or the equivalent input from the Mosaic pipeline)
Relevant Pipelines: APEX Multiframe; APEX Single Frame
Important notes: The user has a choice of two possible input uncertainty images for this module - the std image or the unc image. The choices of input are determined in theAPEX Settings module. See the Discussion below for more information on input image choices.
There is also a choice of several possible data input images into this module, but the difference only becomes significant in a later module, Detect. The reason we mention it here is that this module will carry out the processing on the image specified for input into the Detect module, and the name of the output file will reflect this (see Discussion below). The choice is specified in the APEX Settings module with the Use PSP to Detect parameter.
PURPOSE
This module filters the input co-added image to estimate the probability at each pixel of having a point source above the noise.
INPUT
PRF Resample X(Y) Factor: (int)The ratio of the PRF pixel size to the PRF sampling interval in the x- and y-direction.
PRF X(Y) size: (int) The size of the portion of the PRF image, in input pixels, used to convolve with the input image
Apriori_Probability (float): the lowest probability of a source. It is recommended that it be left to its default of 0.1.
COMMAND LINE INPUT
&POINTSOURCEPROB
PRF_ResampleX_Factor = 4,
PRF_ResampleY_Factor = 4,
PRF_Xsize = 3,
PRF_Ysize = 3,
Noise_Type = 'external_noise',
Apriori_Probability = 0.1,
&END
Noise_Type: (char, command line only) Options are 'external_noise' and 'internal_noise'. The first option requires an uncertainty image, supplied in the Initial Setup. For the second option the noise is estimated from the input image.
OUTPUT
Generated FITS (*_PSP.fits or *_Filtered.fits): The output is the PSP image(s), which shows the point source probability at each pixel. The filename depends on the input image (see Discussion below).
DISCUSSION
This step is performed to improve detectability of the point sources. The filtering is conceptually similar to a convolution of the input image by the PSF, which is commonly done during source extraction. It can be shown that by using the ideas of maximizing SNR in the image, a filter can be derived to estimate the probability at each pixel of having a point source above the noise (see the document Bayesian Estimation of Point Source Probability http://irsa.ipac.caltech.edu/data/SPITZER/docs/files/spitzer/bayesian_estimation_PSP.pdf).
Equation 6.6
Here s is the input background subtracted image, σ is the input uncertainty image, which may be either the mosaic_unc.fits or mosaic_std.fits uncertainty image. This is determined in the APEX Settings module, with the switches Use Uncertainty to Detect and Use Standard Deviation to Detect. If both are set, the first overrides the second. If neither is set, it will calculate the noise internally.
The output of this filter P(j) at pixel j can be interpreted as a probablility of having a point source above the noise at this pixel. The summation is for all pixels i within the area defined by the PRF X(Y) Size parameters. The values of the probability should use the full dynamic range from Apriori_Probability to 1. If the uncertainty is not well estimated it may lead to the output of the filter either not using the whole range or having too many pixels saturated very close to 1. To prevent this from happening, the argument of the exp function is rescaled to utilize the full dynamic range.
There are several possible data input images to this module, but the difference only becomes significant in the later module, Detect. The only reason we mention the following here is that it may affect the name of the output file from this module. The choice of input is specified in the APEX Settings keyword Use PSP to Detect where the options available are Filtered Image, PSP Image (the output of this module) or background subtracted input image. Filtered Image is defined as the product of the PSF image times the background subtracted image: F = P*s. If the Filtered image is used, the name of the output file from this module will be *_Filtered.fits instead of *_PSP.fits. PSP Image uses the output of this module as input into the Detect module, and background subtracted input image uses the original background-subtracted input image for source detection. For more details, see the Detect module.
