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acoadd -- Perform image co-addition and restoration using Lucy Method
acoadd images psfs niter decon coaddr
This task is an implementation of a method developed by Leon Lucy (ST-ECF) for co-adding images which have different point-spread-functions. In addition it may be used as a Richardson-Lucy restoration code with the ability to handle multiple input images. A further useful application is the combination of "dithered" multi-frames. A detailed description of the method and its applications is given in the references mentioned below.
This version incorporates an acceleration option (see below for details of what this does) and the option to start the restoration with a given image. In addition sub-sampling may be handled if a finely sampled version of the PSF is available. There is also an option to allow a mask image indicating the positions of invalid data points.
This version is nominally V1.5 and incorporates some bug-fixes as well as enhancements over V1.4. Note that the parameter names and their meanings have been changed somewhat since the last version. Users are recommended to unlearn the task before using it. An implementation in the MIDAS image processing system is also available via the COADD/IMAGE command in the IMRES context. This version uses similar code but different interface libraries, the results should be identical.
- images = "" [string]
- A list of the images to be co-added, or an image list template. The image dimensions must be even and they must be all the same size. Any negative values found in the images will be set to zero before processing.
- psfs = "" [string]
- A list of the names of the PSFs which match the images.
These images must be the same size and shape as the data images.
The PSFs should be normalised to one (ie, the sum of all the pixels
should be 1.0). The PSFs must be positioned so that PSF 1 convolved with
data frame 1 is aligned with PSF 2 convolved with data frame 2 and so on.
If the peaks of the PSFs are displaced in the same direction as the
shifts in the data frames the alignment will be correct in the output.
In addition the background of the PSF must be removed and the images must be non-negative. Any negative values found in the images will be set to zero before processing.
- niter = [integer]
- The number of iterations to be performed. The Lucy co-addition method is interative and based on the Richardson-Lucy restoration algorithm. It is recommended that a small number (eg, 10) is used for first experiments but the optimum final result for co-addition is normally produced by using the largest value for this parameter that resources permit. For such final production runs the acceleration option is strongly recommended.
- decon = "" [string]
- The name for the output deconvolved image. If this task is being used for normal, or multiple image, restoration this will be the image of interest. It is the result of applying a standard Lucy-Richardson restoration on the data. If this string is set to null no image will be produced, this may be useful if you are primarily interested in the co-added images.
- coaddr = "" [string]
- The root name for the output coadded images. There will be one of these for each input image. They are obtained by convolving the final restored image with each of the PSFs. The names are created by appending _1,'_2' etc to this root name string. If this parameter is null no coadded images will be produced - this may be useful if you are mainly using the task to do image restoration rather than coaddition.
- verbose = "yes" [boolean]
- Whether or not to give frequent information about the progress of the processing. If this is switched on quite a lot of diagnostics are given, when it is off none at all. It is recommended that this be switched on, particularly when using the acceleration option.
- accel = "yes" [boolean]
- Whether or not to use the accelerated algorithm. In this case the correction factor which is applied to the restored image at each iteration is multiplied by a number. This number is such that the increase in likelihood is maximised within the contraint of non-negativity. It is typically between 1 and 10 and leads to considerably faster restoration in most cases. This option is recommended and causes only a small increase in the time taken for each iteration.
- xsubsam = [integer]
- The sub-sampling factor in X. See the examples below for an explanation of how sub-sampled restoration may be performed.
- ysubsam = [integer]
- The sub-sampling factor in Y. See the examples below for an explanation of how sub-sampled restoration may be performed.
- firstim = "" [string]
- This option may be used to start the processing from a known initial guess, or continue processing to further iterations. If this is not specified (ie, set to null) the initial guess will be a flat image with the same total flux as the sum of the input images.
- maskim = "" [string]
- The optional name of an image which acts as a data quality mask. If this image is zero at a given point the data at that point will be ignored, if it is one it will be used. Note that it is a binary mask, not a weighting array. If this is not specified (ie, set to null) the entire image will assumed to be valid data.
1. Simple use of this task to do Lucy deconvolution. If the image is cena and the PSF is psf the result of 20 iterations can be created as cena_dc_20 as follows:
cl> acoadd cena psf 20 cena_dc_20 " "
2. Continue this restoration to another 20 iterations.
cl> acoadd cena psf 20 cena_dc_40 " " firstim=cena_dc_20
3. Coaddition of two frames with acceleration (the default). If the input frames are cena and cenb and the matching PSF images are psfa and psfb then they may be co-added using the command:
cl> acoadd cena,cenb psfa,psfb 20 " " cena_ca
In this case no output deconvolved image will be produced and the co-added images will be cena_ca_1 and cena_ca_2. The acceleration and verbose options will be selected by default.
4. Restoration of a single image with sub-sampling. There are often advantages to creating the restored image on a finer grid than the input data. This application may do such restoration if the PSF is available on a finer grid. The steps in the processing would be:
a) Obtain the PSF on a fine grid. Let's say the PSF on the fine grid is sampled twice as often in X and Y as the original data image and is called psfsub.
b) Block up the data image onto the fine grid by pixel replication. This may be done using a command like:
im> blkrep cena cenasub 2 2
The image cenasub is then on the fine grid (and is twice the size in X and Y).
c) Do the restoration onto a fine grid:
cl> acoadd cenasub psfsub 20 deconsub " " xsubsam=2 ysubsam=2
Typical timings are 40s per iteration per 512 by 512 frame on a SPARCStation 10/51 using the acceleration option, sub-sampling but no data quality mask.
1. The images must have dimensions which are multiples of two. 2. The use of double precision arithmetic throughout makes this task slightly slower than single precision implementations on many machines. 3. A large amount of memory is used and this may limit the array sizes and numbers of arrays which may be handled. 4. World coordinate systems are ignored.
Further information may be found in the following references:
Adorf, H-M., Hook, R.N., Lucy, L.B. & Murtagh F.M., in Proceedings of the 4th ESO/ST-ECF Data Analysis Workshop, Garching, May 1992, p99 [details of acceleration algorithms] Hook, R.N. & Lucy L.B., in Proceedings of the Conference `Science with the Hubble Space Telescope', Sardinia, 1992 [some applications] Lucy, L.B. & Baade, D., in Proceedings of the 1st ESO/ST-ECF Data Analysis Workshop, Garching, April 1989, p219 [subsampling discussion] Lucy, L.B. 1991, ST-ECF Newsletter 16, 6 [original co-adding description] Lucy, L.B., Hook, R.N. 1992, in Proceedings of the 1st Annual Conference on Astronomical Data Analysis Software and Systems, Tucson, November 1991, p277 [more detailed description of the method] Hook, R.N. & Lucy L.B., 1992, ST-ECF Newsletter 17, p10 [applications to some real data] Hook, R.N. & Lucy L.B., 1993, ST-ECF Newsletter 19, p6 [some new bells and whistles] Hook, R.N., 1995, ST-ECF Newsletter 22, p16 [applications to combining sub-stepped WFPC2 data]