TUNING OF ACTIVE DEBLENDING PARAMETERS

K. A. Marsh, IPAC
kam@ipac.caltech.edu

March 29, 2001
(Last update: April 2)



SUMMARY 
 o  Previous work in active deblending has enabled the performance of the 
    algorithm to be characterized in terms of such measures as completeness, 
    reliability, and estimation errors.  The expected benefits of active
    deblending are:

        (1) In crowded fields we can do photometry on many more sources.

	(2) It eliminates the flux bias which would occur if we tried to
	    fit a 2-component source with a single-component model

 o  Current work involves tuning of the parameters involved.  The acceptance
    criteria are reliability-driven, since the cost of an erroneous 2-component
    split is much greater than the cost of cataloging a close double as a 
    single source.  The complete parameter list, together with definitions and 
    recommended values is:

      Maximum number of components:
             adb_nmax   =  2    (Science Team decision, based on cpu 
				 considerations)

      Parameters involved in the decision whether to make a deblend attempt:
          Magnitude cutoff:
             adb_magmax = 14.0 (from chi squared analysis of Version 2 results)

          Chi squared threshold for a deblending attempt:
             adb_chimax = 1.8  (based on the unlikelihood of chi squared < 0.8)

      Acceptance criteria:
          Minimum improvement in chi squared:
              adb_dchi   = 1.0  (based on reliability goal, and successful 
				 deblend fraction)

          Maximum value of the final chi squared:
              chip       = 2.0  (based on the overall histogram of chi squared)

 o  Further work needed:

      (1) Improve the dchi statistics by processing a substantially greater 
	  quantity of data in unconfused (high-latitude) fields.

      (2) Gather more statistics on the fraction of inconsistent deblends
	  (where an inconsistent deblend is defined as one for which the
	  component positions are inconsistent between bands).

      (3) Additional tests as suggested by Science Team.

INTRODUCTION

The performance of the active deblending algorithm, as implemented in PROPHOT, is described in the following documents:

http://spider.ipac.caltech.edu/staff/kam/2mass/deblending/act_real.html (tests with real and synthetic data)

http://spider.ipac.caltech.edu/staff/kam/2mass/deblending/repeat.html (repeatability tests)

The parameters which control deblending are: 

     adb_nmax   =  maximum number of components in an active deblend

     adb_magmax =  maximum magnitude for a deblending attempt

     adb_chimax =  chi squared threshold for a deblending attempt

     adb_dchi   =  minimum improvement in chi squared for a deblend to be
                   accepted

     chip       =  maximum value of the final chi squared for a deblend to be
		   accepted

Based on considerations of computational burden, the 2MASS Science Team decided in mid-2000 that we would limit active deblending to a maximum of two components, i.e. we should set adb_nmax = 2. With regard to the other parameters, J. Rho's analysis of the distribution of chi squared values from Version 2 PROPHOT runs has led to the selection of the following values of adb_magmax and adb_chimax: 

     adb_magmax  =  14.0 (at all 3 bands)

     adb_chimax  =  1.3

The details of this analysis can be found in: http://spider.ipac.caltech.edu/staff/rho/2mass/psfchi/psfchi.html


THE EFFECT OF NEW PSFS

One problem encountered during the chi squared analysis discussed above was the presence of an anomalous trend whereby bright sources had low values of chi squared. This problem was due to shortcomings of the PSFs and variance maps, and was related to another anomalous trend in delta-mag v. magnitude (where delta-mag represents the difference between aperture and profile-fit magnitude). We believe that we have rectified these problems, and accordingly have generated a complete new set of production PSFs for Version 3 processing. Examples of the PROPHOT results for a recent Version 3 RTB run (971116n, s065) are shown in: J-band plot, H-band plot, and K-band plot.

It can be seen that for all 3 bands, the chi squared is centered at unity and shows no trends with magnitude. Based on the Version 3 results to date, the chi squared distributions meet the requirements for deblending.

To keep track of PSF performance, we will add as a system monitor during final processing, plots showing the chi-squared distributions and PSF-aperture magnitude as a function of magnitude, for all sources in a night.


CURRENT WORK ON PARAMETER TUNING

(1) Selection of adb_dchi from reliability considerations.

The key acceptance parameter for the deblending solution is adb_dchi, which represents the minimum acceptable improvement in chi squared as a result of deblending. Setting this parameter involves a compromise between completeness and reliability. Our repeatability tests have demonstrated that setting adb_dchi = 0.5 results in completeness values of 40-50% and reliability values of 95-98%, depending on restrictions imposed with respect to source separation. Since there is a far greater cost attached to the erroneous splitting of a single source as opposed to the converse, the above values of reliability are probably not acceptable. We will therefore adopt a more conservative approach, whereby we set adb_dchi at a value which ensures close to 100% reliability, and let the chips fall where they may with regard to completeness.

In order to select adb_dchi on this basis, we have made histograms of delta-chi values (i.e. the difference between the pre- and post-deblend values of chi squared) for sources believed to be unconfused. For this purpose, we used the following 4 high latitude scans, around glat = 78 deg: 

980416n s008
980416n s012
000116n s058 
000227n s076

For these scans, a set of histograms of delta-chi for sources of magnitude 12 and brighter is shown in delta-chi histograms. From these data, it is apparent that our goal of close to 100% reliability would be satisfied by raising our adb_dchi value to 1.0.

This modification of adb_dchi necessitates a readjustment of adb_chimax (the threshold for an attempted deblend). For example, it would be fruitless to attempt to deblend a source with an initial chi squared of 1.3 since we would only accept the deblending solution if the final chi squared were less than 0.3, a statistically unlikely value. The threshold for deblending (adb_chimax) should therefore be set at a value corresponding to the sum of adb_dchi and the lower limit of likely values of chi squared. To assess the latter, we examine the chi squared distributions, examples of which are shown in J, H, and K histograms, representing the histograms of chi squared values for all sources brighter than 14th magnitude in the above 4 scans. Since the histograms fall off steeply for chi squared < 0.8, it seems reasonable to set adb_chimax to 1.8.


(2) The effect on completeness.

L. Cambresy has carried out an analysis of deblending results from the RTB runs on 971116n. Although the galactic latitudes are mostly high, there is a sufficiently large population of genuinely blended sources for investigating the effect of adb_dchi on completeness.

Histograms of delta-chi values are shown in:

http://spider.ipac.caltech.edu/staff/laurent/QA/Deblend/idl3.ps.

The values plotted represent successful deblends, as defined by consistent component positions among the 3 bands (enabling successful bandmerges). From these plots we can deduce that the effect of raising adb_dchi from 0.5 to 1.0 will be to reduce the completeness to 70%, 69%, and 66% of their former values, at J, H, and K, respectively.

The statistics of unsuccessful deblending solutions can be judged from the following plot:

http://spider.ipac.caltech.edu/staff/laurent/QA/Deblend/idl5.ps.

This plot shows that there is a sharp increase in the fraction of successful deblends at a delta-chi value of 1.0, which is entirely consistent with the conclusions from the previous subsection based on completeness arguments.


(3) Magnitude considerations.

Since H-K takes a fairly narrow range of values for normal stars, an H-K v. K plot gives a useful indication of the behavior of deblending errors as a function of magnitude. For 971116n, we obtain:

http://spider.ipac.caltech.edu/staff/laurent/QA/Deblend/idl1_dchi1.0.ps.

On this plot, inconsistent deblends are indicated by crosses.


CONCLUSIONS REGARDING PARAMETER VALUES

Based on the above considerations, I recommend that we adopt the following parameters for the OPS processing period: 

     adb_nmax   = 2    (Science Team decision, based on cpu considerations)
     adb_magmax = 14.0 (from J. Rho's analysis)
     adb_dchi   = 1.0  (based on reliability goal, and successful deblend fraction)
     adb_chimax = 1.8  (based on the unlikelihood of chi squared < 0.8)
     chip       = 2.0  (based on the overall histogram of chi squared)
These values should result in satisfactory reliability (close to 100%), and will also result in a substantial reduction in computing time as a result of raising the threshold, adb_chimax, at which a deblending attempt will be made. Completeness is expected to fall only to about 70% of the previous value.

We have not introduced a seeing threshold into the deblending criteria, since the results to date do not seem to necessitate it. This is based on the fact that the distributions of delta-chi values do not seem to show any significant differences, at least over ranges of seeing shape factors between 0.98 and 1.21.


WHAT DO WE GAIN FROM DEBLENDING?

(1) In crowded fields we can do photometry on many more sources. Here, for example is a color-color plot of successfully deblended sources from 971116n:

http://spider.ipac.caltech.edu/staff/laurent/QA/Deblend/idl4chi1.ps.

(2) Deblending eliminates a flux bias which would result from trying to fit a single-component model to a dual-component source. Depending on the flux ratio and separation of the components, this bias could be as high as a few tenths of a magnitude. This is discussed in the Sept 29 update to repeatability analysis.

The effect is noticeable if we compare color-color plots with and without deblending. Here is the J-H/H-K plot for the 971116n sources in idl4chi1.ps, but from the Version 2 processing with no deblending:

http://spider.ipac.caltech.edu/staff/laurent/QA/Deblend/idl4_v2.ps.

For comparison, here is the plot obtained by remerging the deblended sources from Version 3 (i.e. adding the deblended fluxes):

http://spider.ipac.caltech.edu/staff/laurent/QA/Deblend/idl4_remerged_chi1.ps.

It is evident that both plots have less scatter than the one for the deblended components (idl4chi1.ps above), reflecting the fact that the total blended flux can be more accurately determined than the fluxes of the individual components. But in addition, the "remerged" deblended plot has significantly less scatter than the Version 2 results, probably due to the elimination of the flux bias mentioned above. It should be noted, however, that some of the outliers in idl4_v2.ps (specifically the ones with H-K < -1) may be due to a passive deblending problem which existed in Version 2, but which was corrected for Version 3.