Image combination techniques

CCDPACK supports many different methods of data combination:

• MEAN
• WEIGHTED MEDIAN
• TRIMMED MEAN
• MODE
• SIGMA CLIPPED MEAN
• THRESHOLD CLIPPED MEAN
• MINIMUM AND MAXIMUM EXCLUSION MEAN
• BROADENED MEDIAN
• SIGMA CLIPPED MEDIAN
• UNWEIGHTED MEDIAN
• DRIZZLE

The aim is to provide you with a fairly exhaustive list of ways in which you can combine your data. The methods include the most efficient (mean) and the most robust (median) estimators and a range of options in between these ideals. A description of the basis of the methods follows:

MEAN

a weighted mean.

WEIGHTED MEDIAN

a weighted median. The weighted average of the values nearest to the half weight value. A more even handed estimator than the ordinary median which takes no account of the errors in the individual measurements.

TRIMMED MEAN

Alpha trimmed mean. The final estimate is the mean of the values excluding the alpha (a fraction between 0 and 0.5) upper and lower values.

MODE

a maximum likelihood mean. This is essentially an iteratively sigma (the standard deviation) clipped mean, where values outside of a given number of sigmas of the mean value are rejected on each pass until convergence is achieved. The standard deviation is always based on the variation of the data contributing to each output value.

SIGMA CLIPPED MEAN

the mean of the values left after rejecting those outside of a given number of standard deviation of the initial mean. The standard deviation is derived from data variances if available, otherwise a standard deviation based on the variation of the data is used.

THRESHOLD CLIPPED MEAN

the mean of the values after rejecting values above and below defined thresholds. Note this usually applies to the output data range if some internal normalisation is performed (MAKEBIAS and MAKEFLAT).

MINIMUM AND MAXIMUM EXCLUSION MEAN

the mean after the
minimum and maximum values are rejected.

BROADENED MEDIAN

the median if the number of input data values is less than five. The mean of the central few values if the number of inputs is larger.

SIGMA CLIPPED MEDIAN

the weighted median of the values left after rejecting those outside of a given number of standard deviations of the initial mean. The standard deviation is derived from data variances if available, otherwise a standard deviation based on the variation of the data is used.

UNWEIGHTED MEDIAN

an unweighted median. A simple median of the data values. No weighting is taken into account. This is significantly faster than the weighted median, but takes no account of the known errors in the measurements.

DRIZZLE

or variable-pixel linear reconstruction, maps weighted input data into pixels in a subsampled output image. In order to avoid convoluting the output image with the large input pixel size, the input pixels are shrunk before it is averaged into the output image.

All of these methods, support variance propagation, provided that the input data errors have an approximately normal distribution.

In general if the input data comprise less than 5 datasets and spurious values are expected to be present, it is very difficult to perform better than the median, and this is the normal default.