Clicking on the Grid Options button in the Main User Interface Menu brings up the Correction Interface Menu shown below.
The menu allows the for various background suppression techniques to be applied to the measured image, solution and zero solution grids, all of which are used in the inversion algorithm. It also allows for definitions of the input parameters for hot spot checking in the solution grid and the line of sight extent used when building the zero solution grid.
The menu is organized according to the algorithms which are available to be applied. Under each algorithm is a list of the grids which it can be applied to. Multiple background suppression algorithms may be applied to a single grid. Then this occurs the algorithms are applied in the order: instrument backgound subtraction, uniform background subtraction, cut background subtraction and despeckling.
In the course of describing the various options below, examples will be included of their effect on a grid. These will all be based on the measured image shown below.
Closes the menu. It can be reopened by clicking on the Corrections button in the main interface menu.
The instrument noise removal algorithm is available for application only on the measured image grid prior to any image smoothing or decimation which make take place. There are a set of four options associated with the algorithm. The Status option toggles between ON and OFF and inticates if the algorithm is to be applied or not. If NO then the remaining three options are ignored. Instrument background is computed column by column in the measured image so that each column has a unique value subtracted from it.
The second option, Location specifies where the background is to be taken from. The options are described below.
| OPTION | DESCRIPTION |
|---|---|
| TOP | The background is accumulated from the top of the image. The accumulation begins at the first row of pixels above maximum phase used in the inversion (above the displayed image above). |
| BOTTOM | The background is accumulated from the bottom of the image. The accumulation begins at the first row of pixels below minimum phase used in the inversion (below the displayed image above). |
| BOTH | The background is accumulated from both the top and bottom of the image. The accumulation begins at the first row of pixels below minimum and above the maximum phases used in the inversion. This is the safest option to use since there are many times when the instrument has be sun safed at the maximim or minimum image phase and the background measured there will be zero! |
The third option, Degrees specifies how many degrees in phase to use in accumulating the backgroun. A value of 0.0 is the same as setting the Status option to OFF and no background subtraction occurs.
The final option, Sigma allows the measured background for each column to be increased or decreased by some fraction of its standard deviation. The algorithm used to determine the final background count in an image column is given by:
The two plots below show the effects of instrument background subtraction on Figure 1 above.
Preconditioning applies only to the measured raw image and occurs only after all of the background removal algorithms defined to be applied to the measuured raw image have been run. There are two preconditioning options, image smoothing and image decimation. Although decimation is the second option listed under preconditioning it is the first applied when both options are selected.
The first option under preconditioning is the smoothing option. The option allows for the measured image to be passed through one of the predefined smoothing filters. The smoothing options are described in the table below.
| OPTION | DESCRIPTION |
|---|---|
| NO | No smoothing filter is defined and the smoothing algorithm is turned off. |
| 3x3L | Image is smoothed using a 3x3 low pass filter. |
| 5x5L | Image is smoothed using a 5x5 low pass filter. |
| 3x3H | Image is smoothed using a 3x3 high pass filter. This is NOT a filter that would normally be used in this circumstance. It is more a boundary sharpening filter which is better suited to smooting the resultant inversion images. |
| 5x5H | Image is smoothed using a 5x5 high pass filter. This is NOT a filter that would normally be used in this circumstance. It is more a boundary sharpening filter which is better suited to smooting the resultant inversion images. |
The second preconditioning option available image decimation. This compresses the image in both dimensions and is in its own right an effect smoothing mechanism. In addition, reducing the image dimensions reduces the time required to complete an inversion and makes it an option often used in test runs. A decimation value of 1 is equivalent to no decimation. A value larger than 1 will reduce the number of pixels in the image in both dimensions by the specified value. A decimation of 2 will reduce the dimension in both directions by 2. The specified decimation does not need to be an integral value. Decimation is performed by regriding the image and NOT by removing lines of pixels.
The figure below shows Figure 2 after decimating it by a factor of 2. In general the image would also have been despeckled prior to smoothing, which has not been done in this case.
There are two general background removal algorithms which are available for use with the raw measured EUV image. In a uniform background removal a single user defined value is subtracted from each cell in the grid. Cell values which go less than zero are set to zero. In a cut background removal all values in the grid which are less than or equal to a user specified threshold are set to 0. A uniform background removal can be used in place of an instrument background removal although this probably would not produce as good results. The cut background removal can be used to remove any cells which have counts in them which are less than one after an instrument background removal. The latter arise since the background values removed from the columns is not required to be an integer value.
The Status option under general background removal toggles between ON and OFF and inticates if the algorithm is to be applied or not. If NO then the Level options on that line is ignored. The Level options are described in the table below.
| TYPE | DESCRIPTION |
|---|---|
| UNIFORM | The specified level value will be subtracted from each cell in the grid. Cell values which become less than zero are set to zero. |
| CUT | All cells in the grid which have a value less than or equal to the specified level will be set to zero. |
The two figures below show examples of the effects of the uniform cut background subtraction on Figure 1. Figure 6 which shows a uniform background subtraction of 5.0 should be compared to Figure 2 which shows Figure 1 after an instrument background subtraction was performed. The cut level used in Figure 7 was 8.0.
Despeckling can be performed on the raw and preconditioned EUV images as well as on the solution and zero solution grids. A despeckling specification consists of 4 options. The first of these is the Status option which toggles between ON and OFF and inticates if the algorithm is to be applied or not to the designated grid.
The second option, Neighbors, is the maximum cluster size to be removed. A value of 0 will reomve pixels which do not contact any other active pixel. A value of 1 will remove all pixels which contact at most one other active pixel, and so on. NOTE: If you abuse this option by setting it to too high a value you can in effect remove your entire image.
The third option in the definition set, Minimum, is the value at which a pixel is considered active. Pixels which have values above this value are considered active. NOTE If you set this value negative you make it look like all pixels are active which effectively turns despeckling. If the value is set too high then it will look like most pixels are inactive which will probably remove more pixels than you want. In general a value between .5 and .99 is adequate for the image and solution grids. Since the zero solution grid only contains values of 0 and 1 you need to set the minimum to a value below 1 as an value above it will turn off every pixel in grid.
The last option in the set, Repeat allows the despeckling algorithm to be run multiple times on an grid. Despeckling can at times reduce larger clusters of pixels to smaller ones which are removed on the second pass.
The following set of plots shows the effects of despeckling on Figure 2 using several different option settings.
Radial noise suppression applies only to the zero solution grid and only if the grid has been defined to be stored in Polar coordinates. Each column in the zero solution grid defines a set of radii at a fixed geomagnetic longitude or equivalently a radial slice through the SM equatoral plane. The algorithm looks along each radial slice for the first N zero values and then assumes that all positions at greater radii must also be zero. (In essence there are no detached blobs.) This works fine so long as there are no plumes which although attached at one point can appear detached along the majority of their extent.
This noise supression technique should be used both sparingly and in general on a case by case inversion and not when inverting multiple images.
The first option under a radial noise definition is the Status option which toggles between ON and OFF and inticates if the algorithm is to be applied or not. The second options is the number of successive zero intensity pixels required to assume that all pixels at larger L should be set to zero.
In the course of the iteration hot spots or instabilities in the solution can arise. They are observed most of the time at the outer edges of the solution; exist over a single pixel; and for the most part correspond to noise or isolated pixels in the measured image. They also are seen to occur at times in grids whose line of sight passes through L-shells which have a defined density arising from a noise pixel. The instability comes about when the iteration tries to fit a set of conditions which can not physically be met. If not treated hot spots can cause the entire solution to be unusable.
The purpose of the hot spot supression algorithm is to identify and correct hot spots before they hit the problem stage. A hot spot is defined as a grid which has a value above some threshold M and which is a factor of N larger then all of its neighbors. When a pixel is flagged as hot, it is set to the average value of its neighbors. This does not address the root cause of the instability and in general the hot spot will reoccur and be corrected in subsequent iteration steps.
There are three options associated with hot spot removal. The first option is the Status option which toggles between ON and OFF and inticates if the algorithm is to be applied or not. The second option, Base defines the minimum value a grid must have before it is subjected to a hot spot check. The final option, Larger By defines the minimum ratio of the value of the pixel being checked to the value of its largest neighbor. If the ratio is greater than this value the pixel is flagged as being a hot pixel and is corrected. Values to 10.0 for the Base and 2.0 to 3.0 for the Larger By option generally five good results.
The zero solution matrix is a mapping of all the locations in the SM equatorial plane which should have a zero He+ density. It is filled in by stepping along the line of sight of each pixel in the measured image which has a zero intensity. At each step the position is converted to the local L value which is then mapped back into the SM equatorial plane and used to set the appropriate cell in the zero solution matrix to 0. The idea is that each L shell which the line of sight passes through must have a zero density associated with it otherwise the pixel would have recorded a signal. The zero solution matrix is used to mask off the positions in the solution matrix which should have a zero intensity.
in principle this should provide an accurate mask and should be a good means of removing noise from the image since non-zero pixels which map to field lines which are deemed to have no He+ intensity on them will be zeroed out. In practice this seems to work well except in cases where there detached or semi-detached features, in particular plumes. Often the extend portion of a plume gets masked out. This would occur if the plume plasma were concentrated about the equatorial plane. In this case lines of sight which passed through the field line above or below the plasma concentration could return zero intensity. The solution would seem to be to limit the tracing of the lines of sight in Z, the distance above and below the SM equatorial plane. While restricting Z somewhat limits the effectiveness or noise removal of the zero solution matrix it does produce a mask which will not zero out the detached features.
The line of sight tracing algorithm has two options. The first option, Max |Z| set the Z limits over which the line of sight is traced. This is from +Z to -Z. The second option specifies the step size to use when tracing out the line of sight. The step size is used to increment Z through the desired range, computing an (X,Y) position for every new Z and from that the local L-shell and the equivalent X,Y position in the SM equatorial plane.
The following three figures show what effect Z has in the construction of the zero solution matrix, especially around semi-detached features. The figure below shows the measured image from Figure 4 but with despeckling applied prior to smoothing and then replotted in the SM equatorial plane. The replotting make it easy to compare the measured image with the zero solution grid which is build in the same coordinate space. Note that in remapping the image there are generally filled cells which are filled using a 2D least squares algorithm. This sometimes will broaden features.
The next two figures show the zero solution grids built from the above plot. The first was formed using a Max Z of .5 and the second using a Max Z of 2.5. Both used a step size of .005 Re. There are two things to note when comparing the two figures. The first is that with the smaller Z the outer extension of the plume near (0.0,5.6) has a non-zero mapping (meaning that density may exist at that location) while this is not the case using the higher Z. The second is that using the higher Z knocks out virtually all the noise seen at X > -3.0 Re which is does not happen with the smaller Z tracing.
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