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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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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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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41 | |
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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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46 | reconstruction: using \texttt{reconDim = 1} makes the reconstruction |
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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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57 | The searching part of the procedure is much quicker: searching an |
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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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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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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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68 | |
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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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77 | reconstruction (\texttt{reconDim = 2}) can be susceptible to edge |
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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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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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96 | many spurious sources (this depends, of course on the cube itself). |
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97 | |
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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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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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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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127 | Finally, as \duchamp is still undergoing development, there are some |
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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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131 | circumvents this problem, but work is being done to make \duchamp |
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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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