Fits independent trends to data lines that are parallel to an axis
The ranges may be determined automatically. There is a choice of tunable approaches to mask regions to be excluded from the fitting to cater for a variety of data sets. The actual ranges used are reported in the current co-ordinate Frame and pixels, provided they apply to all lines being fitted.
Once the trends have been determined they can either be stored directly or subtracted from the input data. If stored directly they can be subtracted later. The advantage of that approach is the subtraction can be undone, but at some cost in efficiency.
Fits may be rejected if their root-mean squared (rms) residuals are more than a specified number of standard deviations from the the mean rms residuals of the fits. Rejected fits appear as bad pixels in the output data.
Fitting independent trends can be useful when you need to remove the continuum from a spectral cube, where each spectrum is independent of the others (that is you need an independent continuum determination for each position on the sky). It can also be used to de-trend individual spectra and perform functions like debiassing a CCD which has bias strips.
TRUE
, the
ranges that define the trends are determined automatically, and Parameter RANGES is
ignored. [FALSE]
Its integer index within the current Frame of the input NDF (in the range 1 to the number of axes in the current Frame).
Its Symbol string such as "RA"
or "VRAD"
.
A generic option where "SPEC"
requests the spectral axis, "TIME"
selects the time axis,
"SKYLON"
and "SKYLAT"
picks the sky longitude and latitude axes respectively. Only
those axis domains present are available as options.
A list of acceptable values is displayed if an illegal value is supplied. If the axes
of the current Frame are not parallel to the NDF pixel axes, then the pixel axis which
is most nearly parallel to the specified current Frame axis will be used. AXIS defaults
to the last axis. [!]
TRUE
. Its purpose is to exclude features that are not part of the
trends.
Pixels are rejected at the $i$th
clipping cycle if they lie beyond plus or minus
CLIP($i$)
times the dispersion about the mediaan of the remaining good pixels. Thus lower values
of CLIP will reject more pixels. The normal approach is to start low and progressivley
increase the clipping factors, as the dispersion decreases after the exclusion of
features. The source of the dispersion depends on the value the METHOD parameter.
Between one and five values may be supplied. Supplying the null value (!
), results in
2, 2.5, and 3 clipping factors. [2,2,2.5,3]
"Polynomial"
for a polynomial or "Spline"
for a
bi-cubic B-spline. ["Polynomial"]
TRUE
if the data may contain spectral data with many lines–-a line forest–-when
using the automatic range mode (AUTO=TRUE
). A different approach using the
histogram determines the baseline mode and noise better in the presence of multiple
lines. This leads to improved masking of the spectral lines and affords a better
determination of the baseline. In a lineforest the ratio of baseline to line
regions is much reduced and hence normal sigma clipping, when FOREST=FALSE
,
is biased. [FALSE]
"Spline"
. See INTERPOL for how the knots are arranged. The default is the
current value.
For INTERPOL=TRUE
, the value must be in the range 1 to 11, and 4
is a reasonable value
for flatish trends. The initial default is 4
.
For INTERPOL=FALSE
the allowed range is 1 to 60 with an initial default of 8
. In this
mode, KNOTS is the maximum number of interior knots.
The upper limit of acceptable values for a trend axis is no more than half of the axis
dimension. []
TRUE
. "Spline"
.
If set TRUE
, an interpolating spline is fitted by least squares that ensures the fit is
exact at the knots. Therefore the knot locations may be set by the POSKNOT
parameter.
If set FALSE
, a smoothing spline is fitted. A smoothing factor controls the degree of
smoothing. The factor is determined iteratively between limits, hence it is the slower
option of the two, but generally gives better fits, especially for curvy trends. The
location of of the knots is decided automatically by Dierckx’s algorithm, governed
where they are most needed. Knots are added when the weighted sum of the squared
residuals exceeds the smoothing factor. A final fit is made with the chosen smoothing,
but finding the knots afresh.
The few iterations commence from the upper limit and progress more slowly at each iteration towards the lower limit. The iterations continue until the residuals stabilise or the maximum number of interior knots is reached or the lower limit is reached. The upper limit is the weighted sum of the squares of the residuals of the least-squares cubic polynomial fit. The lower limit is the estimation of the overall noise obtained from a clipped mean the standard deviation in short segments that diminish bias arising from the shape of the trend. The lower limit prevents too many knots being created and fitting to the noise or fine features.
The iteration to a smooth fit makes a smoothing spline somewhat slower. [FALSE]
"Single"
or "Global"
. It has the
same bounds as the input NDF and the data array is type _BYTE. No mask NDF is
created if null (!
) is supplied. [!]
"Region"
–- This averages trend lines from a selected representative region given by
Parameter SECTION and bins neighbouring elements within this average line. Then it
performs a linear fit upon the binned line, and rejects the outliers, iteratively with
standard-deviation clipping (Parameter CLIP). The standard deviation is that of
the average line within the region. The ranges are the intervals between the
rejected points, rescaled to the original pixels. They are returned in Parameter
ARANGES.
This is best suited to a low dispersion along the trend axis and a single concentrated region containing the bulk of the signal to be excluded from the trend fitting.
"Single"
–- This is like "Region"
except there is neither averaging of lines nor a
single set of ranges. Each line is masked independently. The dispersion for
the clipping of outliers within a line is the standard deviation within that
line.
This is more appropriate when the features being masked vary widely across the image, and significantly between adjacent lines. Some prior smoothing or background tracing (CUPID: FINDBACK) will usually prove beneficial.
"Global"
–- This is a variant of "Single"
. The only difference is that the dispersion
used to reject features using the standard deviation of the whole data array. This is
more robust than "Single"
, however it does not perform rejections well for lines with
anomalous noise.
["Single"]
TRUE
. If MODIFYIN is FALSE
,
then an NDF name must be supplied by the OUT parameter. [FALSE]
16
, and the maximum is such that there will be a factor of two compression.
NUMBIN is ignored when there are fewer than 32 elements in each line to be
de-trended. [32]
0
is a constant and 1
a
line, 2
a quadratic etc. The maximum value is 15
. ORDER is only accessed when
FITTYPE="Polynomial"
. [3]
TRUE
(in
that case the input NDF will be modified). !
) value to request equally spaced knots. The units of
these co-ordinates is determined by the axis of the current world co-ordinate
system of the input NDF that corresponds to the trend axis. Supplying a colon
":"
will display details of the current co-ordinate Frame. [!]
FALSE
. If PROPBAD is TRUE
, the returned
fitted values are set bad if the corresponding input value is bad. If PROPBAD is
FALSE
, the fitted values are retained. [TRUE]
!
), causes all the values along each data line to be used. The units of these
ranges is determined by the axis of the current world co-ordinate system of
the input NDF that corresponds to the trend axis. Supplying a colon ":"
will
display details of the current co-ordinate Frame. Up to ten pairs of values
are allowed. This parameter is not accessed when AUTO=TRUE
. [!]
!
) means perform no rejections. Allowed values are between 2 and 15.
[!]
TRUE
, METHOD= "Region"
, and the dimensionality of
the input NDF is more than 1. The value is defined as an NDF section, so that
ranges can be defined along any axis, and be given as pixel indices or axis
(data) co-ordinates. The pixel axis corresponding to parameter AXIS is ignored.
So for example, if the pixel axis were 3 in a cube, the value "3:5,4,"
would
average all the lines in elements in columns 3 to 5 and row 4. See Section 9 for
details.
A null value (!
) requests that a representative region around the centre be used. [!]
[FALSE]
[!]
TRUE
and the input NDF contains
variances, then the polynomial or spline fits will be weighted by the variances. TRUE
, recording the trend-axis fitting regions determined automatically. They
comprise pairs of pixel co-ordinates. This application attempts to solve the problem of fitting numerous polynomials in a least-squares sense and that do not follow the natural ordering of the NDF data, in the most CPU-time-efficient way possible.
To do this requires the use of additional memory (of order one fewer than the dimensionality of the NDF itself, times the polynomial order squared). To minimise the use of memory and get the fastest possible determinations you should not use weighting and assert that the input data do not have any BAD values (use the application SETBAD to set the appropriate flag).
If you choose to use the automatic range determination. You may need to determine
empirically what are the best clipping limits, binning factor, and for METHOD="Region"
the region to average.
You are advised to inspect the fits, especially the spline fits or high-order polynomials. A given set of trends may require more than one pass through this task, if they exhibit varied morphologies. Use masking or NDF sections to select different regions that are fit with different parameters. The various trend maps are then integrated with PASTE to form the final composite set of trends that you can subtract.
This routine correctly processes the AXIS, DATA, QUALITY, LABEL, TITLE, UNITS, HISTORY, WCS, and VARIANCE components of an NDF data structure and propagates all extensions.
Processing of bad pixels and automatic quality masking are supported.
All non-complex numeric data types can be handled.
Handles data of up to 7 dimensions.