wtransform

Synopsis

Obtain wavelet transform coefficients for poisson image data

wtransform  infile srclist correl nbkg [bkg] [thresh] [outputinfix]
[exptime] [expfile] [expcor] [expthresh] [bkgtime] [bkginput]
[bkgerrinput] [xscales] [yscales] [clobber] [correlerr] [nbkgerr]
[bkgerr] [maxiter] [iterstop] [sigthresh] [bkgsigthresh] [falsesrc]
[sigcalfile] [log] [verbose] [stall]

Description

`wtransform' performs detection on a dataset by repeatedly correlating it with "Mexican Hat" wavelet functions with different scale sizes. At each scale, wtransform starts with the original image, and correlates it with the wavelet. Pixels with sufficiently large positive correlation values are removed from the image (as assumed sources), and subsequent correlations are performed at the same scale. This procedure of extracting source pixels from an image is called "cleansing". Typically, when very few source candidates are being found, or when an iteration-count limit is reached, the cleansing process stops. At this point, the estimated background (estimated from the cleansed image) is used to set detection thresholds, which are applied to the initial correlation image array values to identify putative sources. A set of outputs for the given wavelet scale is generated: a table of candidate sources (identified by correlation maxima), an image of the correlation of the data with the wavelet function, an image of the normalized (or flat-field) background (the image minus the "source" pixels), and the normalized background error image. Then the tool moves on to the next scale and repeats the process with a fresh copy of the image.

Note: As a stand-alone tool, wtransform is only intended for use by those with a thorough understanding of the wavelet detection process. Most users should use the `wavdetect' script.

This tool requires a lot of memory. Data structures for a 512x512 image use up 36 meg. A 2048x2048 images requires over 300 meg. Data sets that do not fit in physical memory will page heavily to disk and processing will run very slowly.

Each cleansing iteration is time-consuming.

See: "WDETECT and WRECON: Wavelet Transform Techniques for Spatial Analysis of AXAF Data" Freeman, Kashyap, Rosner, Lamb. HEAD '97 Conference

For a more complete description of the theory and operation of wavdetect, please see the wavdetect sections of the CIAO Detect Manual.

Example

wtransform pleiades.fits pleiades_src_stk.lis pleiades_correl_stk.lis
pleiades_nbkg_stk.lis xscales="1 2 4 8 16" yscales="1 2 4 8 16"

Read a primary image from "pleiades.fits". Write a series of source candidate list files, named in "pleiades_src_stk.lis". Write a series of correlation images, named in "pleiades_correl_stk.lis". Write a series of normalized background images, named in "pleiades_nbkg_stk.lis". Examine the input (and generate outputs) at pixel scales 1 2 4 8 and 16.

For other wavdetect examples, please see the CIAO Science Thread "Running wavdetect".

Parameters

Detailed Parameter Descriptions

Parameter=infile (file required filetype=input)

Input file

If the input data are not a FITS primary image, this name must include the extension, eg: "foo.fits[EVENTS]".

Parameter=srclist (file required filetype=output autoname=yes)

File name for stack (list) of per-scale candidate source output files.

If auto-naming is used (srclist=.), the output file will have the suffix "_src_stk"

Parameter=correl (string required filetype=output autoname=yes)

Name of file to contain stack (list) of per-scale correlation output images.

If auto-naming is used (correl=.), the output file will have the suffix "_correl_stk"

Parameter=nbkg (string required filetype=output autoname=yes)

File name of stack (list) of normalized (i.e. flat-field) background output images created at each scale.

If auto-naming is used (nbkg=.), the output file will have the suffix "_nbkg_stk"

Parameter=bkg (string filetype=output default= autoname=yes)

Name of file to contain stack (list) of per-scale plain background images. Set to "none" to disable.

If auto-naming is used (bkg=.), the output file will have the suffix "_bkg_stk".

Parameter=thresh (string filetype=output default= autoname=yes)

File name of stack (list) of per-scale source detection correlation threshold output images.

If auto-naming is used (thresh=.), the output file will have the suffix "_thresh_stk".

Parameter=outputinfix (file default=)

Leave blank. This parameter controls extra text to insert in output filenames. for internal use only.

Parameter=exptime (real default=0 min= units=seconds)

Time of the exposure, in seconds. If set to zero, the program estimates the exposure time from the exposure map.

Parameter=expfile (string filetype=input default=)

Image of exposure time for dataset.

Parameter=expcor (string default=fast)

Fast or Full or None. Correct for obstructions and vignetting in the telescope. "none"=no corrections. If in doubt, use the "fast" correction.

"full": assume C_correct = C_measured - avg(W*(EB_norm)) + avg(W*B_norm)E C = correlation, at pixel in question E = exposure B_norm = normalized background W = wavelet function avg(W*(EB_norm)) equal to or greater than correlation of wavelet function and product of exposure and normalized background, at pixel in question avg(W*B_norm) equal to or greater than correlation of wavelet function and normalized background This correction is applied during each iteration, since B_norm changes. "fast": assume C_correct = C_measured - B_norm * avg(W*E)

Parameter=expthresh (real default=0.1 min= max=)

For each pixel, a relative exposure is calculated (pixel exposure time over detector livetime). If this relative exposure is less than the parameter expthresh, then the pixel in question is not analyzed: the background, correlation, et al., are set to zero.

expthresh should not be less than 0.1 (or else the accuracy of normalization will be too low); if set close to 1, only very limited regions of the FOV will be considered when source correlation maxima are listed. Typical values would be 0.1-0.2.

Parameter=bkgtime (real default=0 min= units=seconds)

Livetime of predetermined background.

This parameter is only used *if* the user has provided a normalized background image. A value of 0 means use the exposure time as the background time.

Parameter=bkginput (string not required filetype=input default=)

Pre-determined background input image.

Use a previously computed background in the specified file in place of constructing new per-scale normalized backgrounds.

Parameter=bkgerrinput (boolean not required default=no)

If yes, use background error in file bkginput[2].

Parameter=xscales (string default=2.0 units=pixels)

The wavelet scale sizes in the x direction, given by pixel values in this list of numbers.

The number of scale sizes (a series of numbers separated by spaces) indicated by xscales must be the same as yscales. The scale sizes themselves for a particular run do not have to be equal, though initial usage of asymmetric wavelets is not advised.

Wtransform produces a complete set of outputs for each scale. Small scales tend to detect small features, and larger scales larger features.

Values are typically 2**n, where n is an integer, and n_lo and n_hi are chosen with respect to instrumental PSF sizes. For the ROSAT PSPC, for instance, this could mean n_lo = 1 pixel, n_hi = 16 pixels. Note that larger scales might need to be used to characterize (i.e. derive good source property estimates for) extended sources.

2**n should not be larger than the size of the image (in pixels) divided by 5 (in which case the extent of the wavelet function is larger than the image itself, which could lead to strange results).

Parameter=yscales (string default=2.0 units=pixels)

The wavelet scale size in the y direction, given by pixel values in this list of numbers.

The number of scale sizes indicated by yscales must be the same as xscales. See additional notes under 'xscales'.

Parameter=clobber (boolean default=no)

If "yes", existing outputs will be overwritten.

Parameter=correlerr (boolean default=yes)

If set to "yes", wtransform will include an error image as part of the correlation image.

Parameter=nbkgerr (boolean default=yes)

If set to "yes", wtransform will include an error image as part of the normalized background images (these outputs are needed by wrecon).

Parameter=bkgerr (boolean default=no)

If set to "yes", wtransform will include an error image as part of the plain background image.

Parameter=maxiter (integer default=2 min=)

Maximum number of cleansing iterations per scale pair. 4 is usually adequate. If the maxiter is greater than necessary, the program will usually stop on its own (see iterstop).

Parameter=iterstop (real default=0.0001 min= max=)

The user specifies how many iterations the program should go through to calculate the background (parameter iters).

The user specifies how many iterations the program should go through to calculate the background. However, the background is for all intents and purposes calculated if there are very few new pixels being cleansed (see bkgsigthresh). If the ratio of *newly* cleansed pixels to the overall number of pixels in the mask is less than the parameter iterstop, the program quits iterating and uses the current background estimate as the final background estimate.

A typical value is 0.0001: stop iterating when only one of every ten thousand pixels is being cleansed. This parameter should not be larger than 1, nor smaller than one over the number of pixels in the image/mask.

Parameter=sigthresh (real default=1e-06 min= max=)

*After* the final background estimate B_final is made, the threshold correlation is recomputed by solving for C_o: sigthresh = integral(C_o dC) PSD(C(B_final))

*After* the final background estimate B_final is made, the threshold correlation is recomputed by solving for C_o: sigthresh = integral(C_o dC) PSD(C(B_final))

Here, C = avg(W*D), where D are the *raw* data. (The iterations are simply to compute background. Once we have that, we go back to the beginning.)

If C is greater than or equal to C_o in a pixel, then that pixel is considered to be associated with a source. If the pixel is also the location of a local maximum in C-space, the location of that maximum is output to a FITS table.

sigthresh should not be significantly larger than one over the number of pixels in the image/mask; for a 1024x1024 image, that means sigthresh ~ 1.e-6. If, in this case, sigthresh = 1.e-5, there will be approximately 10 strong background fluctuations detected as sources.

sigthresh should not be smaller than *roughly* 1.e-9 - 1.e-10; even at this point, the accuracy of the computed detection thresholds is unknown (though probably fine for most applications).

Parameter=bkgsigthresh (real default=0.001 min= max=)

Significance threshold for cleansing data during iterations.

In each pixel, during each iteration, the background, and correlation of the wavelet function and the current data (C' = avg(W*D')), are estimated. The background estimate B' implies a probability sampling distribution (PSD) for C', i.e. the distribution that C' would have if there was locally no source in the image and D' were sampled from background. A threshold C_o' is calculated from this PSD, using the supplied value of bkgsigthresh (e.g. 0.01) by solving the following for C_o':

bkgsigthresh = integral(C_o' dC') PSD(C'(B'))

If

C' is greater than or equal to C_o'

, the data in the pixel is replaced with the background estimate. In this way, putative sources are eliminated from the data image, along with weak (but otherwise undetectable) sources and background fluctuations, so that a better background estimate can be made.

This value should be no larger than 0.05 (the usual 5%, or 95%, statistical criterion for rejecting the null hypothesis, which is that the pixel in question has data sampled solely from the background); it should not be smaller than sigthresh.

Parameter=falsesrc (real not required default=-1.0)

Number of false sources allowed per scale in the image.

That number is combined with image size and scale information, using additional simulation results contained in the file defined by the sigcalfile parameter, to determine the threshold significance for each pixel; consequently the value given for the parameter sigthresh is ignored. If falsesrc is set to a negative number, the code uses sigthresh instead to determine thresholds.

Parameter=sigcalfile (file not required filetype=ARD default=$ASCDS_CALIB/wtsimresult.fits)

Data file for use by the false-source algorithm.

The file contains simulation results that are used with the false-source algorithm. This file is included with with the release and may be used for both Chandra and non-Chandra data. The user may not specify "CALDB" for this parameter.

Parameter=log (boolean default=no)

If set to "no", log information will go to stdout. If set to "yes", file "wtransform.log" will be created.

Parameter=verbose (integer default=0 min=0 max=5)

Level of debugging output

Parameter=stall (boolean default=no)

Special mode to rendezvous a debugger with wtransform. Leave set to "no".

Changes in CIAO 4.16

• Some error handling cleanup.

• Corrected the units from "degrees" to "deg" as per the FITS standard.

Bugs

There are no known bugs for this tool.

See Also

tools::background

create_bkg_map

tools::detect

celldetect, vtpdetect, wavdetect, wrecon

tools::gratings

tgdetect, tgidselectsrc, tgmatchsrc

tools::region

rank_roi, regphystocel, roi, splitroi