A general technique to improve the spatial resolution of the IRAS AO data was developed at The Aerospace Corporation using the Maximum Entropy algorithm of Skilling and Gull. The technique has been applied to a variety of fields and several individual AO MACROS. With this general technique, resolutions of 15 arcsec were achieved in 12 and 25 micron images and 30 arcsec in 60 and 100 micron images. Results on galactic plane fields show that both photometric and positional accuracy achieved in the general IRAS survey are also achieved in the reconstructed images

Canterna, R.

Dyck, H. Melvin

Grasdalen, Gary L.

Hackwell, John A.

Inguva, R.

English

NASA Technical Reports Server

NASA-CR-199506 ^»
FINAL REPORT
HIGH SPATIAL RESOLUTION RESTORATION OF IRAS
IMAGES
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Principal Investigators:
Gary L. Grasdalen, PI
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H. Melviii Dyck
R. Canterna
The Department of Physics and Astronomy
University of Wyoming
Laramie, Wyoming 82071
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ABSTRACT
A general technique to improve the spatial resolution of the
IRAS AO data was developed at The Aerospace Corporation using the
Maximum Entropy algorithm of Skilling and Gull. The technique has
been applied to a variety of fields and several individual AO
MACROS. With this general technique, resolutions of 15 arcsec were
achieved in 12 and 25 p.m images and 30 arcsec in 60 and 100 /im
images. Results on galactic plane fields show that both
photometric and positional accuracy achieved in the general IRAS
survey are also achieved in the reconstructed .images.
GENERAL TECHNIQUE
To improve the spatial resolution of the IRAS data, two major
problems must be solved. The most severe problem is the unevenly
spaced nature of the IRAS data. Most algorithms treat this problem
by interpolating the original data onto an evenly spaced grid
before applying any enhancement procedure. Cosmic ray hits or
detector hysteresis compromise this interpolation process. The
second problem is the adequate characterization of detector
response. This includes the non-linearity of the detectors over
several orders of magnitude in flux, their -hysteresis, and an
adequate description of the point response functions (PRFs) of the
individual detectors. We will address the first of these problems
and demonstrate the Aerospace/Wyoming solution as applied to the AO
data for the galactic plane field GS0513 and the star formation
region HH 1/2.
The Aerospace/Wyoming technique is a sufficiently general one
that can be applied to multi-detector data and used with a wide
variety of non-linear image reconstruction algorithms. It has been
successfully applied to close contact, point source galaxies,
nearby extended galaxies, star formation regions, rich cirrus
fields, and the galactic plane.
As an illustration of the technique we will demonstrate the
procedure for one of the simplest of AO macros, DSD01A. The DSD01A
macro has 18 scans at one-half the survey speed of length 28 arc
min. The scans are separated by a cross-scan step of 0.5 arc min
(Young et al. 1985). This IRAS macro centers the four small side
detectors #47 (Band 1 = 12 microns), #39 (Band 2 = 25 microns), #31
(Band 3 = 60 microns) , and #55 (Band 4 = 100 microns) on the region
of interest, although all of the detectors are taking data. The
placement of the detectors in the IRAS focal plane is shown in
Figure 1.
The detector data positions for all four bands in image space
are presented in figure 2 for the star formation region HH 1/2.
The rectangular areas in each plot are the physical dimensions of
each detector. At 12 and 60 microns the data are slightly under-
sampled in the cross-scan direction and over-sampled in the in-scan
direction. At 25 and 100 microns both dimensions are over-sampled.
For multi-detector macros, regions of interests may have areas
where detector data points overlap each other. For these cases the
Aerospace/Wyoming method treats each detector with its own unique
point response function and does not assume an average PRF.
A new approach to the general problem of applying non-linear
techniques for image reconstruction and multi-dimensional data
analysis on unevenly spaced data was developed with the constraints
placed upon the technique by Jaynes's Axiom (Jaynes 1985): The
first thing to do with the data is to convolve it with the point
response function. Let f represent the observations, which is a
result of the convolution of the instrumental.function, g , and
reality, r , plus a noise term, n, i.e.
f = g * r + n
where * is the convolution operator.
Since most non-linear and maximum likelihood schemes typically
seek solutions that satisfy a least-squares criterion, Jaynes's
Axiom becomes quite obvious. Generally, solutions to the inverse
problem require that the function H will be minimized, where
H = S; (g * r - f)1" 2
The condition for minimization leads directly to the condition
= 0 = 2 (g* * g * r - g* * f),
To apply this general solution to the IRAS data a general
response matrix, R, is created which "blurs" the data with the
response functions of"the individual detectors and at the same time
re-grids the unevenly-spaced data into an evenly-sampled image
space. The general response matrix, R, is uniquely determined by
the detector response functions and the detector positions. R can
then be substituted for g in our general least-squares criterion
which now becomes
(Rf * R * r - R1 * f) =0
where RR* is the transpose of the response matrix. Each data point
has a unique weight, therefore no interpolation of the data is
required.
If there are N; image points on an evenly-space image grid and
Nd data points on the unevenly-space data grid, then the response
matrix is N, x Nd. For a 32 x 32 image with N; = 1024, Nd may be «
1000, and the response matrix has 106 entries. Using this
approach, images up to 200 x 300 pixels have been restored using
the individual point response functions and individual noise
figures for each of the detectors. For the HH1/2 region only one
detector per band was used and a 40 x 80 pixel image was produced
at 15 arc sec per pixel. For a typical galactic plane region all
working detectors were used and a 150 x 250 image was produced at
15 arc sec per pixel, depending on the macro. Using a Micro-VAX II
microprocessor with an array processor, real speeds of 3
megaflops/sec were achieved. Recently preliminary images on a
galactic plane field took over 20 hours of CPU time to complete 20
iterations.
The Gull and Skilling (1984) maximum entropy program has been
used exclusively for these data. Our novel approach will also work
for the Willingale (1981) and Lucy (1974) algorithms, but we feel
that the maximum entropy method provides us with the most unbiased,
best estimate of reality. The final image must meet two
criterion: it must satisfy a chi squared constraint, due to maximum
likelihood, and a maximum entropy constraint. Convergence
therefore depends only on the best estimate of the noise vector and
is not a subjective decision of the operator.
To initiate the reduction of the observations we take the
the AO Calibrated Raw De-tector Data (CRDD) for each band and use
the following procedure.
a. Since the scans were not always parallel to the N-S or E-
W equatorial axes, the data grid was rotated around the
central reference position thus aligning the image grid
parallel to the in-scan direction. This makes
construction of the response matrix much simpler and
leads to faster mathematical operations.
b. All cosmic ray hits or other spurious data were
eliminated from the data set.
c. The two-dimensional background was set to zero. This
correction also included corrections for any background
gradients; e.g. zodiacal light, diffuse cirrus. A de-
striping routine is applied initially to the eliminate
any scan-to-scan background variation.
A global estimate of the noise was determined from
source-free regions in each band. This global noise is
determined by the standard deviation of the differences
in intensity between two adjacent points for each scan
leg. Values more than three standard deviations are
rejected and a new final value for the noise for each
scan leg is then recalculated.
For regions with sources two terms are added in
quadrature with the global noise: the first term
is directly related to the gradient of the flux, to
account for positional errors; and the second term
is directly related to the signal, to account for
the non-linearity of- the detector signal.
The data and noise estimates were then processed in the
maximum entropy algorithm until convergence was obtained.
PUBLICATIONS
"A General Technique for Recovering High Angular Resolution
Images from Unevenly-Spaced Data", J. A. Hackwell, L. M.
Friesen, R. Canterna, and G. L. Grasdalen, 1988, BAAS, 20.
677.
"High Resolution Observations of the HH1 and HH2 Region with
IRAS", Hackwell, J. A., Grasdalen, G., L., Canterna, R., and
Friesen, L. M., 1988, Workshop on the Formation and Evolution
of Planetary Systems.
"Star Counts in the Galactic Plane from High Spatial
Resolution Images from IRAS". 1988, BAAS, 20, 1018
" High Spatial-Resolution Images of M 51" in The Second
Wyoming Conference on The Interstellar Medium in External
Galaxies, Jackson Hole, WY. by Canterna,R., Hackwell, J. A.,
and Grasdalen, G. L.
"Infrared Sources in the Galactic. Disk from Image-Recovered
IRAS data", by R. Canterna, J. Hackwell, G. Grasdalen, R.
Hermann, and S. Gillam. In preparation, will be submitted to
Ap. J.
" The Infrared Source Counts in the Galactic Thin Disk
Population from High-Spatial resolution IRAS Images" , by A.
Evans, R. Hermann, R. Canterna, and J. Hackwell. Present at
January 1990 AAS meeting, Washington DC
" Infrared Studies of the Galactic Plane I: The IRAS Disk
Population at 1 = 30°", by Canterna, R. Hackwell, J.A. ,
Hermann, R. , and Grasdalen, G. L. , (Submitted for publication)
"A General Technique for Recovering High Angular Resolution
Images from Unevenly-Spaced Data", J. A. Hackwell, L. M.
Friesen, R. Canterna, and G. L. Grasdalen, In preparation.
Star Counts in the Galactic Plane from High Spatial Resolution
Images from IRAS.
R. Canterna (Wyoming Infrared Obs. [WIRO] and The Aerospace
Corporation [A.C.]), John A. Hackwell (A.C.)/ Gary L. Grasdalen,
Rob Hermann, and Steve Gillam (WIRO).
The 0.5 x 0.75 galactic plane field (IRAS identification GS0513)
centered around 1= 29.3 and b = -0.1 have been analyzed using
several IRAS data bases. High spatial resolution images have been
recovered for the same field from AO CRDD data using the general
techniques for image recovery discussed by Hackwell, Friesen,
Canterna, and Grasdalen (BAAS 20, p677) and the maximum entropy
method described by Gull and Skilling (IEE Proc (F), 131. p646).
The reconstructed images have been used to form star counts as a
function of flux for bands 1 and 2 and the results are compared
with the IRAS Serendipitous and Point Source Catalogs and the
Regridded AO images for the same field. In addition to revealing
additional point sources above the Point Source Catalog (PSC)
confusion level of 2 Jy, the recovered, images have also revealed
more than a factor of 2 more point sources below the PSC confusion
level. Monte Carlo calculations have been made to model the
galactic plane structure and are compared with observations.
The InfraRed Source Counts in the Galactic Thin Disk
Population from High-Spatial Resolution IRAS Images.
Aaron Evans (U. Michigan/Wyoming Infrared Observatory [WIRO]), Rob
Hermann, R. Canterna (WIRO/The Aerospace Corporation), and J.A.
Hackwell (The Aerospace Corporation).
ABSTRACT
Two galactic plane fields ( 1= 21.8°, b = - 3°; 1= 29.3° b=
-0.1°have been analyzed from high spatial-resolution images of IRAS
calibrated raw detector data using the general recovery method
developed by Hackwell, Friesen, Canterna, and Grasdalen and the
Gull/Skilling Maximum Entropy technique. We have been able to
resolve multiple sources at all flux levels, especially in the
cross-scan direction. In both areas over a factor of 2.5 more
sources than is recorded in the Point Source Catalog have been
discovered, resulting in a complete sample, flux limited to 0.8 Jy.
Flux levels down to 0.4 Jy have been measured in one area.
Photometric precision similar to the IRAS PSC has been achieved at
all flux levels. Source counts supports evidence for a 1.3° thin
disk population with a scale height of < 170 pc. The 12 and 25 urn
color data show evidence of a very red population, quite different
than the normal bulge and disk IRAS population.
INTRODUCTION
The true nature and description of the IRAS point source counts
within the galactic plane is not well known. The confusion-
limited regions for the IRAS Point Source Catalog (PSC) along the
galactic plane are a result of more complicated effects than those
implied by classic concepts of source confusion due to excessive
source densities. The detection threshold for the PSC is raised
in the galactic plane because the estimated noise is increased
above the intrinsic detector noise by the large number of point
sources per scan. Additional skewing is introduced by the
trailing noise estimator used by the PSC algorithms. The
estimator, which uses a preceding portion of the scan data to
obtain a local noise estimate, underestimates the noise when
entering the plane and overestimates the noise when leaving -the
confused region. This shadowing and memory effect add to the
extreme complexities of the confusion region centered on the
galactic plane. We can reduce this problem by applying new
imaging techniques to IRAS fields.
HIGH SPATIAL RESOLUTION IMAGES OF IRAS GALACTIC PLANE FIELDS.
We have applied a general technique of recovering high angular
resolution images to the unevenly-spaced original IRAS Additional
Observation (AO) Calibrated Re-constructed Detector Data (CRDD)
(Hackwell, Friesen, Canterna, and Grasdalen 1988; hereafter
referred to as "The Aerospace Method"). The Aerospace method uses
the maximum entropy algorithm of Gull and Skilling (1984). The
final "super-resolution" images of two fields have been analyzed
and compared the results from the PSC. Figure 1 shows a
comparison of the IRAS survey field and a blow-up of our
reconstructed field.
Our data shows an increased number of IRAS sources in the galactic
plane. We have investigated the IRAS AO fields GS0513 and
GS0960. GS0513 is centered at 1=29.3° and b = -0.1°. The
area analyzed is approximately 0.3° x 0.75°. The AO macro for
this field (DPS60D) was raster scanned at half the survey rate,
with a scan length of 60 arc minutes, cross-scan of 0.8 arc
minutes, and 4 scans per macro. GS0960 is centered at 1 = 21.8°
b = -0.3° [area is 0.8° x 0.6°]. The AO macro
was DSD01A, which was a raster scan at half the survey rate with a
scan length of 28 arc minutes, cross-scan of 0.5 arc min, and 18
scans per macro.
RESULTS
In Figure 2 a plot of the logarithm the accumulative number of
sources per square degree versus the logarithm of the 12 juu m
source flux in Jy is presented for field GS0513. The dotted line
is the results from high 12 jum flux quality sources from the
PSC and the solid line is from our reconstructed images. From an
analysis of our high spatial resolution images
• multiple sources are clearly separated.
• a factor of 2 or more point sources have been detected.
• a completeness flux level less than 1.0 Jy is achieved.
THE NATURE OF THE INFRARED THIN DISK POPULATION
The 12 p.m completeness flux level for galactic longitude 30° is
approximately 1.8 Jy. In Figures 3 and 4 the natural logarithm of
the number of sources per square degree with high 12 micron flux
quality greater than 2.0 Jy is plotted against galactic latitude
within a 1 degree band centered on 1 = 30°. The results from our
reconstructed image is also plotted, showing the consistency
between our results and the PSC for this flux limit. A thick 3°
galactic disk model can be fitted to the data .with a 1.4° THIN
disk component superimposed. The nature of this thin disk
component is seen in Figure 4 where the relative number of sources
per square degree are plotted as a function of color (ratio of 12
to 25 micron fluxes) for sources between galactic longitudes -3 to
-10 degrees. A similar relation is found for galactic longitudes
+3 to +10. In an overlay we plot the same relation for galactic
plane field GS0960 where we have analyzed both 12 and 25 micron
"super-resolution" images. On sees that the thin disk population
has color temperatures that are significantly cooler than the
thick disk population.


High spatial resolution restoration of IRAS images

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