[303] | 1 | % ----------------------------------------------------------------------- |
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| 2 | % hints.tex: Section giving some tips & hints on how Duchamp is best |
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| 3 | % used. |
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| 4 | % ----------------------------------------------------------------------- |
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| 5 | % Copyright (C) 2006, Matthew Whiting, ATNF |
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| 6 | % |
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| 7 | % This program is free software; you can redistribute it and/or modify it |
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| 8 | % under the terms of the GNU General Public License as published by the |
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| 9 | % Free Software Foundation; either version 2 of the License, or (at your |
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| 10 | % option) any later version. |
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| 11 | % |
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| 12 | % Duchamp is distributed in the hope that it will be useful, but WITHOUT |
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| 13 | % ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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| 14 | % FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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| 15 | % for more details. |
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| 16 | % |
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| 17 | % You should have received a copy of the GNU General Public License |
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| 18 | % along with Duchamp; if not, write to the Free Software Foundation, |
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| 19 | % Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA |
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| 20 | % |
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| 21 | % Correspondence concerning Duchamp may be directed to: |
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| 22 | % Internet email: Matthew.Whiting [at] atnf.csiro.au |
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| 23 | % Postal address: Dr. Matthew Whiting |
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| 24 | % Australia Telescope National Facility, CSIRO |
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| 25 | % PO Box 76 |
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| 26 | % Epping NSW 1710 |
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| 27 | % AUSTRALIA |
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| 28 | % ----------------------------------------------------------------------- |
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[158] | 29 | \secA{Notes and hints on the use of \duchamp} |
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| 30 | \label{sec-notes} |
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| 31 | |
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| 32 | In using \duchamp, the user has to make a number of decisions about |
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| 33 | the way the program runs. This section is designed to give the user |
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| 34 | some idea about what to choose. |
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| 35 | |
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[285] | 36 | The main choice is whether to alter the cube to try and enhance the |
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| 37 | detectability of objects, by either smoothing or reconstructing via |
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| 38 | the \atrous method. The main benefits of both methods are the marked |
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| 39 | reduction in the noise level, leading to regularly-shaped detections, |
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| 40 | and good reliability for faint sources. |
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[158] | 41 | |
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[285] | 42 | The main drawback with the \atrous method is the long execution time: |
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| 43 | to reconstruct a $170\times160\times1024$ (\hipass) cube often |
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| 44 | requires three iterations and takes about 20-25 minutes to run |
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| 45 | completely. Note that this is for the more complete three-dimensional |
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[298] | 46 | reconstruction: using \texttt{reconDim = 1} makes the reconstruction |
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[285] | 47 | quicker (the full program then takes less than 5 minutes), but it is |
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| 48 | still the largest part of the time. |
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| 49 | |
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| 50 | The smoothing procedure is computationally simpler, and thus quicker, |
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| 51 | than the reconstruction. The spectral Hanning method adds only a very |
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| 52 | small overhead on the execution, and the spatial Gaussian method, |
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| 53 | while taking longer, will be done (for the above example) in less than |
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| 54 | 2 minutes. Note that these times will depend on the size of the |
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| 55 | filter/kernel used: a larger filter means more calculations. |
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| 56 | |
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[158] | 57 | The searching part of the procedure is much quicker: searching an |
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[285] | 58 | un-reconstructed cube leads to execution times of less than a |
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| 59 | minute. Alternatively, using the ability to read in previously-saved |
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[158] | 60 | reconstructed arrays makes running the reconstruction more than once a |
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| 61 | more feasible prospect. |
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| 62 | |
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| 63 | On the positive side, the shape of the detections in a cube that has |
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[285] | 64 | been reconstructed or smoothed will be much more regular and smooth -- |
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| 65 | the ragged edges that objects in the raw cube possess are smoothed by |
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| 66 | the removal of most of the noise. This enables better determination of |
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| 67 | the shapes and characteristics of objects. |
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[158] | 68 | |
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[292] | 69 | While the time overhead is larger for the reconstruction case, it will |
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| 70 | potentially provide a better recovery of real sources than the |
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| 71 | smoothing case. This is because it probes the full range of scales |
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| 72 | present in the cube (or spectral domain), rather than the specific |
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| 73 | scale determined by the Hanning filter or Gaussian kernel used in the |
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| 74 | smoothing. |
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| 75 | |
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| 76 | When considering the reconstruction method, note that the 2D |
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[298] | 77 | reconstruction (\texttt{reconDim = 2}) can be susceptible to edge |
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[292] | 78 | effects. If the valid area in the cube (\ie the part that is not |
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| 79 | BLANK) has non-rectangular edges, the convolution can produce |
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| 80 | artefacts in the reconstruction that mimic the edges and can lead |
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| 81 | (depending on the selection threshold) to some spurious |
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[158] | 82 | sources. Caution is advised with such data -- the user is advised to |
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| 83 | check carefully the reconstructed cube for the presence of such |
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| 84 | artefacts. Note, however, that the 1- and 3-dimensional |
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| 85 | reconstructions are \emph{not} susceptible in the same way, since the |
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| 86 | spectral direction does not generally exhibit these BLANK edges, and |
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| 87 | so we recommend the use of either of these. |
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| 88 | |
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| 89 | If one chooses the reconstruction method, a further decision is |
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| 90 | required on the signal-to-noise cutoff used in determining acceptable |
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| 91 | wavelet coefficients. A larger value will remove more noise from the |
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| 92 | cube, at the expense of losing fainter sources, while a smaller value |
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| 93 | will include more noise, which may produce spurious detections, but |
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| 94 | will be more sensitive to faint sources. Values of less than about |
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| 95 | $3\sigma$ tend to not reduce the noise a great deal and can lead to |
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[160] | 96 | many spurious sources (this depends, of course on the cube itself). |
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[158] | 97 | |
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[285] | 98 | The smoothing options have less parameters to consider: basically just |
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| 99 | the size of the smoothing function or kernel. Spectrally smoothing |
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| 100 | with a Hanning filter of width 3 (the smallest possible) is very |
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| 101 | efficient at removing spurious one-channel objects that may result |
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| 102 | just from statistical fluctuations of the noise. One may want to use |
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| 103 | larger widths or kernels of larger size to look for features of a |
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| 104 | particular scale in the cube. |
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| 105 | |
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[158] | 106 | When it comes to searching, the FDR method produces more reliable |
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| 107 | results than simple sigma-clipping, particularly in the absence of |
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| 108 | reconstruction. However, it does not work in exactly the way one |
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| 109 | would expect for a given value of \texttt{alpha}. For instance, |
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| 110 | setting fairly liberal values of \texttt{alpha} (say, 0.1) will often |
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| 111 | lead to a much smaller fraction of false detections (\ie much less |
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| 112 | than 10\%). This is the effect of the merging algorithms, that combine |
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| 113 | the sources after the detection stage, and reject detections not |
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| 114 | meeting the minimum pixel or channel requirements. It is thus better |
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| 115 | to aim for larger \texttt{alpha} values than those derived from a |
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| 116 | straight conversion of the desired false detection rate. |
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| 117 | |
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[292] | 118 | If the FDR method is not used, caution is required when choosing the |
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| 119 | S/N cutoff. Typical cubes have very large numbers of pixels, so even |
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| 120 | an apparently large cutoff will still result in a not-insignificant |
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| 121 | number of detections simply due to random fluctuations of the noise |
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| 122 | background. For instance, a $4\sigma$ threshold on a cube of Gaussian |
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| 123 | noise of size $100\times100\times1024$ will result in $\sim340$ |
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| 124 | detections. This is where the minimum channel and pixel requirements |
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| 125 | are important in rejecting spurious detections. |
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| 126 | |
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[258] | 127 | Finally, as \duchamp is still undergoing development, there are some |
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[158] | 128 | elements that are not fully developed. In particular, it is not as |
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| 129 | clever as I would like at avoiding interference. The ability to place |
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| 130 | requirements on the minimum number of channels and pixels partially |
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[258] | 131 | circumvents this problem, but work is being done to make \duchamp |
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[158] | 132 | smarter at rejecting signals that are clearly (to a human eye at |
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| 133 | least) interference. See the following section for further |
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| 134 | improvements that are planned. |
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