Weekly Report 19Nov2010 26Nov2010

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(RHESSI Image Test - Clean v. Pixon)
(RHESSI Image Test - Clean v. Pixon)
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I've looked at multiple configurations for the original data map and the flux measurement is usually wrong if multiple sources are present, regardless of the imaging algorithm. If the original sources are compact and separated, clean and pixon can image the size of the source down to the 50% contour pretty well, but do a poor job of reproducing the flux in each source. This may be due to the fact that the  algorithms do not preserve the total counts in the original eventlist used. Is this constraint not used because it restricts the algorithm too much while it is iterating and prevents it from converging to an image?
I've looked at multiple configurations for the original data map and the flux measurement is usually wrong if multiple sources are present, regardless of the imaging algorithm. If the original sources are compact and separated, clean and pixon can image the size of the source down to the 50% contour pretty well, but do a poor job of reproducing the flux in each source. This may be due to the fact that the  algorithms do not preserve the total counts in the original eventlist used. Is this constraint not used because it restricts the algorithm too much while it is iterating and prevents it from converging to an image?
For an unknown image the flux measurements of a source are difficult to trust, the size can be determined but it requires using multiple detector configurations and comparing them.
For an unknown image the flux measurements of a source are difficult to trust, the size can be determined but it requires using multiple detector configurations and comparing them.
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The lastest save file for the imaging test is present [http://hesperia.gsfc.nasa.gov/~agopie/kontar_sim_albedo/clean_sim_maps_best_attempt_clean_new_0123456789.sav here]
+
The latest save file for the imaging test is present [http://hesperia.gsfc.nasa.gov/~agopie/kontar_sim_albedo/clean_sim_maps_best_attempt_clean_new_0123456789.sav here]
===RHESSI Website Migration===
===RHESSI Website Migration===

Revision as of 16:55, 30 November 2010

Contents

Pixon Albedo Imaging

Using Eduard Kontar's simulated eventlist files, Pixon Images were created for a compact circular gaussian source with an albedo contribution near disk center, and near the limb. The following parameters were used for each image:

The following plots are extensions of the plots from the previous report.

The plot below shows the gaussian model of the compact source (orange),the original data map with the minimum and maximum value at each radial distance (Black), the Pixon image with the minimum and maximum value at each radial distance (Purple), and the clean image with the minimum and maximum value at each radial distance (Cyan)for a source near disk center.

Original Data Map (Black), Pixon Map (Purple), Clean Map (Cyan), Model Gaussian (orange) for a source near the disk center

The gaussian model falls off as we would expect the flux to fall in a circular gaussian. For 2 arcsec the model and the original map are consistent, after this point the model falls off much more sharply, while the original map shows a falloff that is not gaussian. Obviously this is what we expect, once we enter the region where the albedo is dominant a simple single gaussian model will not model the compact source plus the extended source. The pixon image shows a tight envelope around the compact source, as does the clean image. As we move into the region where the albedo is present clean falls off in the same manner as the original map. The envelope around the the average of the flux for clean widens immediately after the compact source but then remains relatively constant. The pixon image immediately goes from a tight envelope around the compact source to a wider envelope in the region of the albedo. The size of the envelope remains constant radially but the average moves up and down in an unpredictable manner. For instance at approximately 3.5 arcsec from the peak of the compact source, pixon images what appears to be a 'pileup' of flux. At the edges of the image the flux does not drop away to zero but seems to level off for pixon. This seems to be a characteristic of pixon, and shows up in all pixon images for a compact source with albedo, in a field of view that is a few square arcsecs larger than the original map.


The plot below shows the gaussian model of the compact source (orange),the original data map with the minimum and maximum value at each radial distance (Black), the Pixon image with the minimum and maximum value at each radial distance (Purple), and the clean image with the minimum and maximum value at each radial distance (Cyan) for a source near the limb.

Original Data Map (Black), Pixon Map (Purple), Clean Map (Cyan), Model Gaussian (orange) for a source near the limb)

In the case of the source near the limb the averages of each the original data, the clean image, and the pixon image fall off in a similar manner to the averages near the disk center. There is more variation at any given point, with the average moving up and down, but the trend is similar. However, looking at the min and max for the original data map, and the imaging algorithms the foreshortening effect shows up. There is a much larger envelope around the average for each method. The min and the max are much more widely separated. The min falls off to zero more rapidly and the max is higher in each case, at a given radial distance. This is what we would expect in the case of foreshortening. Foreshortening creates an asymmetry in the source and the albedo. The plots below clearly show this asymmetry.

The following plot shows the the average and the min and max for the clean images near the disk center and near the limb.

The clean profile for an image near disk center (Cyan), and near the limb (Purple), with the minimum and maximum values also shown for each radial distance.

The purple plot shows the values for the image near disk center. The cyan plot shows the image near the limb. The image near the disk center shows a tight envelope around the average value for the extent of the compact source. As we move radially away from the compact source the envelope around the average flux gets wider but remains symmetric. Looking at the cyan plot, the average flux away from the compact source falls of slightly more than near disk center, but with a similar slope. It does not fall off in the same smooth fashion as the image near disk center, showing higher and lower fluxes as it approaches the edge of image causing a 'spiky' pattern. The more interesting aspect is the behavior of the min and max traces. The envelope formed by these around the average is wider than in the case of the image at disk center, with a sharper falloff for the minimum compared to the maximum. This is the expected behavior when foreshortening is present.The minimum values at a given radial distance away from the disk center will be smaller than the values toward the disk center. This means the minimum value and maximum values should differ more than in a case with radial symmetry. This demonstrates that near the limb, at a given distance from the radial compact source, flux at one point will be higher than at a point that is mirrored around the Y symmetric axis through the compact source. Although no information about the position of the min and max in the heliocentric X position is contained in this plot we can infer this from previous plots of the flux profiles along a line through the image in the X direction.


The following plot shows the the average and the min and max for the clean images near the disk center and near the limb.

The pixon profile for an image near disk center (Cyan), and near the limb (Purple), with the minimum and maximum values also shown for each radial distance.

The purple traces above show the profile for the image near the limb, while the cyan plots show the image near disk center. The first obvious difference between the clean images and the pixon images is the flux at the center of the pixon images. The foreshortened image has a higher flux at the center than the source near disk center. The source near the disk center shows a tighter envelope around the compact source which increases slightly in flux away from the source but remains symmetric and compact, although the falloff is not smooth, showing various spikes such as the one at ~ 3.5 arcsec from the compact source. The source near the limb shows the min and the max diverging immediately away from the center of the compact source. The average starts to match the average of the source near disk center as we enter the region were the albedo is present. The differences are in the min and max. The minimum shows a drop away from the average, but the difference between pixon and clean shows up here. Clean drops to zero in the minimum immediately away from the compact source. Pixon still shows a small contribution from the albedo in the minimum for the image. The maximum falls off more smoothly than clean which shows some spikes in the maximum than a falloff.

Currently it seems that Pixon can do a good job of imaging the foreshortening of the source and the albedo, it is much less clear that direct imaging of the albedo is possible with pixon. It depends on the level of albedo contribution compared to the compact source flux. At the 1% level pixon does not seem to successfully directly image the albedo.

RHESSI Image Test - Clean v. Pixon

The following is an example from the RHESSI Imaging Test. The original map is two compact sources, 20 arcsecs apart, 2 arcsecs in extent. The plot below shows the original map as the background image, the pixon contours in blue (using d1 to d4), and the clean contours in green, (using a clean beam width factor of 2, with d1 and d2).

The original source map (background), with the pixon contours(Blue) for an image using detectors 1 to 4, and clean contours (Green) for an image using detectors 1 and 2.

In the case above the contours are all at the default percentage levels. The pixon contours at the 10% level are larger in extent than the same level for clean. This is due in part to pixon breaking down if only detectors 1 and 2 are used, while with clean, the image was made with only detector 1 and 2. At contours above the 50% level both methods do a good job of getting the correct size and shape of the original map.

The plot below shows the flux profile for the original data map (Black), the clean image (Red), and the pixon image (Green), along a line parallel to the heliocentric X axis through the line symmetry of the original map in that direction.

The profile in the Heliocentric X direction through the center of the map. The profile for the original map is black, the clean profile is red, and the green profile is red.

The original map shows two peaks which are symmetric and 20 arcsecs apart. The clean profile and the pixon profile are both slightly offset from the center of the original data map. The peaks are offset toward the disk center by ~ 1 arcsec. Another difference between the images and the original data map is the relative flux of the two sources. In the original map the flux is equal for both sources. Clean shows a similar value of the flux for the source closer to disk center but the flux for the second source is approximately ~10% lower. Pixon shows the flux for both sources at a lower value than the original map, with the source farther away from disk center having a higher value. I've looked at multiple configurations for the original data map and the flux measurement is usually wrong if multiple sources are present, regardless of the imaging algorithm. If the original sources are compact and separated, clean and pixon can image the size of the source down to the 50% contour pretty well, but do a poor job of reproducing the flux in each source. This may be due to the fact that the algorithms do not preserve the total counts in the original eventlist used. Is this constraint not used because it restricts the algorithm too much while it is iterating and prevents it from converging to an image? For an unknown image the flux measurements of a source are difficult to trust, the size can be determined but it requires using multiple detector configurations and comparing them. The latest save file for the imaging test is present here

RHESSI Website Migration

The new RHESSI website now has more content and increased functionality for adding various kinds of content. The filelist module has been added and various documents and images have been uploaded. These are now available for use on any page on the website. A news reader has also installed that allows rotating news to be placed on any page. A similar image plugin was added, allowing a gallery to be setup on the back end from which images can be automatically displayed on pages at given times. A reader has been added that can link to external content such as the nuggets and update pages on the rhessi website.

Currently I am working on the appearance of the pages, for instance the publications page has content but the appearance needs to be upgrade. The home page and the documentation page are currently the only pages left to update.

Goals for Next Week

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