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 | \secB{Memory usage} |
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37 | |
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38 | A lot of attention has been paid to the memory usage in \duchamp, |
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39 | recognising that data cubes are going to be increasing in size with |
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40 | new generation correlators and wider fields of view. However, users |
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41 | with large cubes should be aware of the likely usage for different |
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42 | modes of operation and plan their \duchamp execution carefully. |
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43 | |
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44 | At the start of the program, memory is allocated sufficient for: |
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45 | \begin{itemize} |
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46 | \item The entire pixel array (as requested, subject to any |
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47 | subsection). |
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48 | \item The spatial extent, which holds the map of detected pixels (for |
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49 | output into the detection map). |
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50 | \item If smoothing or reconstruction has been selected, another array |
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51 | of the same size as the pixel array. This will hold the |
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52 | smoothed/reconstructed array (the original needs to be kept to do the |
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53 | correct parameterisation of detected sources). |
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54 | \item If baseline-subtraction has been selected, a further array of |
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55 | the same size as the pixel array. This holds the baseline values, |
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56 | which need to be added back in prior to parameterisation. |
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57 | \end{itemize} |
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58 | All of these will be float type, except for the detection map, which |
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59 | is short. |
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60 | |
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61 | There will, of course, be additional allocation during the course of |
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62 | the program. The detection list will progressively grow, with each |
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63 | detection having a memory footprint as described in |
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64 | \S\ref{sec-scan}. But perhaps more important and with a larger |
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65 | impact will be the temporary space allocated for various algorithms. |
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66 | |
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67 | The largest of these will be the wavelet reconstruction. This will |
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68 | require an additional allocation of twice the size of the array being |
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69 | reconstructed, one for the coefficients and one for the wavelets - |
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70 | each scale will overwrite the previous one. So, for the 1D case, this |
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71 | means an additional allocation of twice the spectral dimension (since |
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72 | we only reconstruct one spectrum at a time), but the 3D case will |
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73 | require an additional allocation of twice the cube size (this means |
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74 | there needs to be available at least four times the size of the input |
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75 | cube for 3D reconstruction, plus the additional overheads of |
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76 | detections and so forth). |
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77 | |
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78 | The smoothing has less of an impact, since it only operates on the |
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79 | lower dimensions, but it will make an additional allocation of twice |
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80 | the relevant size (spectral dimension for spectral smoothing, or |
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81 | spatial image size for the spatial Gaussian smoothing). |
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82 | |
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83 | The other large allocation of temporary space will be for calculating |
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84 | robust statistics. The median-based calculations require at least |
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85 | partial sorting of the data, and so cannot be done on the original |
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86 | image cube. This is done for the entire cube and so the temporary |
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87 | memory increase can be large. |
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88 | |
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89 | |
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90 | \secB{Timing considerations} |
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91 | |
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92 | Another intersting question from a user's perspective is how long you |
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93 | can expect \duchamp to take. This is a difficult question to answer in |
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94 | general, as different users will have different sized data sets, as |
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95 | well as machines with different capabilities (in terms of the CPU |
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96 | speed and I/O \& memory bandwidths). Additionally, the time required |
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97 | will depend slightly on the number of sources found and their size |
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98 | (very large sources can take a while to fully parameterise). |
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99 | |
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100 | Having said that, in \citet{whiting12} a brief analysis was done |
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101 | looking at different modes of execution applied to a single HIPASS |
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102 | cube (\#201) using a MacBook Pro (2.66GHz, 8MB RAM). Two sets of |
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103 | thresholds were used, either $10^8$~Jy~beam$^{-1}$ (no sources will be |
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104 | found, so that the time taken is dominated by preprocessing), or |
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105 | 35~mJy~beam$^{-1}$ (or $\sim2.58\sigma$, chosen so that the time taken |
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106 | will include that required to process sources). The basic searches, |
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107 | with no pre-processing done, took less than a second for the |
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108 | high-threshold search, but between 1 and 3~min for the low-threshold |
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109 | case -- the numbers of sources detected ranged from 3000 (rejecting |
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110 | sources with less than 3 channels and 2 spatial pixels) to 42000 |
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111 | (keeping all sources). |
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112 | |
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113 | When smoothing, the raw time for the spectral smoothing was only a few |
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114 | seconds, with a small dependence on the width of the smoothing |
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115 | filter. And because the number of spurious sources is markedly |
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116 | decreased (the final catalogues ranged from 17 to 174 sources, |
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117 | depending on the width of the smoothing), searching with the low |
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118 | threshold did not add much more than a second to the time. The spatial |
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119 | smoothing was more computationally intensive, taking about 4 minutes |
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120 | to complete the high-threshold search. |
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121 | |
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122 | The wavelet reconstruction time primarily depended on the |
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123 | dimensionality of the reconstruction, with the 1D taking 20~s, the 2D |
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124 | taking 30 - 40~s and the 3D taking 2 - 4~min. The spread in times for |
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125 | a given dimensionality was caused by different reconstruction |
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126 | thresholds, with lower thresholds taking longer (since more pixels are |
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127 | above the threshold and so need to be added to the final spectrum). In |
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128 | all cases the reconstruction time dominated the total time for the |
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129 | low-threshold search, since the number of sources found was again |
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130 | smaller than the basic searches. |
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131 | |
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132 | |
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133 | \secB{Why do preprocessing?} |
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134 | |
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135 | The preprocessing options provided by \duchamp, particularly the |
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136 | ability to smooth or reconstruct via multi-resolution wavelet |
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137 | decomposition, provide an opportunity to beat the effects of the |
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138 | random noise that will be present in the data. This noise will |
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139 | ultimately limit ones ability to detect objects and form a complete |
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140 | and reliable catalogue. Two effects are important here. First, the |
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141 | noise reduces the completeness of the final catalogue by suppressing |
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142 | the flux of real sources such that they fall below the detection |
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143 | threshold. Secondly, the noise provides false positive detections |
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144 | through noise peaks that fall above the threshold, thereby reducing |
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145 | the reliability of the catalogue. |
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146 | |
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147 | \citet{whiting12} examined the effect on completeness and reliability |
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148 | for the reconstruction and smoothing (1D cases only) when applied to a |
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149 | simple simulated dataset. Both had the effect of reducing the number |
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150 | of spurious sources, which means the searches can be done to fainter |
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151 | thresholds. This led to completeness levels of about one flux unit |
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152 | (equal to one standard-deviation of the noise) fainter than searches |
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153 | without pre-processing, with $>95\%$ reliability. The smoothing did |
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154 | slightly better, with the completeness level nearly half a flux unit |
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155 | fainter than the reconstruction, although this was helped by the |
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156 | sources in the simulation all having the same spectral size. |
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157 | |
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158 | \secB{Reconstruction considerations} |
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159 | |
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160 | The \atrous wavelet reconstruction approach is designed to remove a |
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161 | large amount of random noise while preserving as much structure as |
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162 | possible on the full range of spatial and/or spectral scales present |
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163 | in the data. While it is relatively more expensive in terms of memory |
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164 | and CPU usage (see previous sections), its effect on, in particular, |
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165 | the reliability of the final catalogue makes it worth investigating. |
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166 | |
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167 | There are, however, a number of subtleties to it that need to be |
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168 | considered by potential users. \citet{whiting12} shows a set of |
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169 | examples of reconstruction applied to simulated and real data. The |
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170 | real data, in this case a HIPASS cube, shows differences in the |
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171 | quality of the reconstructed spectrum depending on the dimensionality |
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172 | of the reconstruction. The two-dimensional reconstruction (where the |
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173 | cube is reconstructed one channel map at a time) shows much larger |
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174 | channel-to-channel noise, with a number of narrow peaks surviving the |
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175 | reconstruction process. The problem here is that there are spatial |
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176 | correlations between pixels due to the beam, which allow beam-sized |
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177 | noise fluctuations to rise above the threshold more frequently in |
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178 | one-dimension. The other effect is that when compared to a spectrum |
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179 | from the 1D reconstruction, each channel is independently |
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180 | reconstructed, and does not depend on its neighbouring channels. This |
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181 | is also why the 3D reconstruction (which also suffers from the beam |
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182 | effects) has improved noise in the output spectrum, since the |
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183 | information on neighbouring channels is taken into account. |
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184 | |
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185 | Caution is also advised when looking at subsections of a cube. Due to |
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186 | the multi-scale nature of the algorithm, the wavelet coefficients at a |
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187 | given pixel are influenced by pixels at very large separations, |
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188 | particularly given that edges are dealt with by assuming reflection |
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189 | (so the whole array is visible to all pixels). Also, if one decreases |
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190 | the dimensions of the array being reconstructed, there may be fewer |
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191 | scales used in the reconstruction. These points mean that the |
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192 | reconstruction of a subsection of a cube will differ from the same |
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193 | subsection of the reconstructed cube. The difference may be small |
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194 | (depending on the relative size difference and the amount of structure |
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195 | at large scales), but there will be differences at some level. |
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196 | |
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197 | Note also that BLANK pixels have no effect on the reconstruction: they |
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198 | remain as BLANK in the output, and do not contribute to the discrete |
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199 | convolution when they otherwise would. The use of the Milky Way |
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200 | channel range, however, has no effect on the reconstruction -- these |
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201 | are applied after the preprocessing, either in the searching or the |
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202 | rejection stage. |
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203 | |
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204 | \secB{Smoothing considerations} |
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205 | |
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206 | The smoothing approach differs from the wavelet reconstruction in that |
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207 | it has a single scale associated with it. The user has two choices to |
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208 | make - which dimension to smooth in (spatially or spectrally), and |
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209 | what size kernel to smooth with. \citet{whiting12} show examples of |
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210 | how different smoothing widths (in one-dimension in this case) can |
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211 | highlight sources of different sizes. If one has some \textit{a |
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212 | priori} idea of the typical size scale of objects one wishes to |
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213 | detect, then choosing a single smoothing scale can be quite |
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214 | beneficial. |
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215 | |
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216 | Note also that beam effects can be important here too, when smoothing |
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217 | spatial data on scales close to that of the beam. This can enhance |
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218 | beam-sized noise fluctuations and potentially introduce spurious |
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219 | sources. As always, examining the smoothed array (after saving via |
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220 | \texttt{flagOutputSmooth}) is a good idea. |
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221 | |
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222 | |
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223 | \secB{Threshold method} |
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224 | |
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225 | When it comes to searching, the FDR method produces more reliable |
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226 | results than simple sigma-clipping, particularly in the absence of |
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227 | reconstruction. However, it does not work in exactly the way one |
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228 | would expect for a given value of \texttt{alpha}. For instance, |
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229 | setting fairly liberal values of \texttt{alpha} (say, 0.1) will often |
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230 | lead to a much smaller fraction of false detections (\ie much less |
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231 | than 10\%). This is the effect of the merging algorithms, that combine |
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232 | the sources after the detection stage, and reject detections not |
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233 | meeting the minimum pixel or channel requirements. It is thus better |
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234 | to aim for larger \texttt{alpha} values than those derived from a |
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235 | straight conversion of the desired false detection rate. |
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236 | |
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237 | If the FDR method is not used, caution is required when choosing the |
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238 | S/N cutoff. Typical cubes have very large numbers of pixels, so even |
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239 | an apparently large cutoff will still result in a not-insignificant |
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240 | number of detections simply due to random fluctuations of the noise |
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241 | background. For instance, a $4\sigma$ threshold on a cube of Gaussian |
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242 | noise of size $100\times100\times1024$ will result in $\sim340$ |
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243 | single-pixel detections. This is where the minimum channel and pixel |
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244 | requirements are important in rejecting spurious detections. |
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245 | |
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246 | |
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247 | % \secB{Preprocessing} |
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248 | % |
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249 | % \secC{Should I do any preprocessing?} |
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250 | % |
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251 | % The main choice is whether to alter the cube to try and enhance the |
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252 | % detectability of objects, by either smoothing or reconstructing via |
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253 | % the \atrous method. The main benefits of both methods are the marked |
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254 | % reduction in the noise level, leading to regularly-shaped detections, |
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255 | % and good reliability for faint sources. |
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256 | % |
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257 | % The main drawback with the \atrous method is the long execution time: |
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258 | % to reconstruct a $170\times160\times1024$ (\hipass) cube often |
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259 | % requires three iterations and takes about 20-25 minutes to run |
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260 | % completely. Note that this is for the more complete three-dimensional |
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261 | % reconstruction: using \texttt{reconDim = 1} makes the reconstruction |
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262 | % quicker (the full program then takes less than 5 minutes), but it is |
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263 | % still the largest part of the time. |
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264 | % |
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265 | % The smoothing procedure is computationally simpler, and thus quicker, |
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266 | % than the reconstruction. The spectral Hanning method adds only a very |
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267 | % small overhead on the execution, and the spatial Gaussian method, |
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268 | % while taking longer, will be done (for the above example) in less than |
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269 | % 2 minutes. Note that these times will depend on the size of the |
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270 | % filter/kernel used: a larger filter means more calculations. |
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271 | % |
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272 | % The searching part of the procedure is much quicker: searching an |
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273 | % un-reconstructed cube leads to execution times of less than a |
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274 | % minute. Alternatively, using the ability to read in previously-saved |
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275 | % reconstructed arrays makes running the reconstruction more than once a |
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276 | % more feasible prospect. |
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277 | % |
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278 | % On the positive side, the shape of the detections in a cube that has |
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279 | % been reconstructed or smoothed will be much more regular and smooth -- |
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280 | % the ragged edges that objects in the raw cube possess are smoothed by |
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281 | % the removal of most of the noise. This enables better determination of |
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282 | % the shapes and characteristics of objects. |
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283 | % |
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284 | % \secC{Reconstruction vs Smoothing} |
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285 | % |
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286 | % While the time overhead is larger for the reconstruction case, it will |
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287 | % potentially provide a better recovery of real sources than the |
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288 | % smoothing case. This is because it probes the full range of scales |
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289 | % present in the cube (or spectral domain), rather than the specific |
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290 | % scale determined by the Hanning filter or Gaussian kernel used in the |
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291 | % smoothing. |
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292 | % |
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293 | % When considering the reconstruction method, note that the 2D |
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294 | % reconstruction (\texttt{reconDim = 2}) can be susceptible to edge |
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295 | % effects. If the valid area in the cube (\ie the part that is not |
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296 | % BLANK) has non-rectangular edges, the convolution can produce |
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297 | % artefacts in the reconstruction that mimic the edges and can lead |
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298 | % (depending on the selection threshold) to some spurious |
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299 | % sources. Caution is advised with such data -- the user is advised to |
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300 | % check carefully the reconstructed cube for the presence of such |
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301 | % artefacts. |
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302 | % |
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303 | % A more important effect that can be important for 2D reconstructions |
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304 | % is the fact that the pixels in the spatial domain typically exhibit |
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305 | % some correlation due to the beam. Since each channel is reconstructed |
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306 | % independently, beam-sized noise fluctuations can rise above the |
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307 | % reconstruction threshold more frequency than in the 1D case, providing |
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308 | % a greater number of spurious single-channel spikes in a given |
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309 | % reconstructed spectrum. This effect will also be present in 3D |
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310 | % reconstructions, although to a lesser degree since information in the |
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311 | % spectral direction is also taken into account. |
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312 | % |
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313 | % If one chooses the reconstruction method, a further decision is |
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314 | % required on the signal-to-noise cutoff used in determining acceptable |
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315 | % wavelet coefficients. A larger value will remove more noise from the |
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316 | % cube, at the expense of losing fainter sources, while a smaller value |
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317 | % will include more noise, which may produce spurious detections, but |
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318 | % will be more sensitive to faint sources. Values of less than about |
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319 | % $3\sigma$ tend to not reduce the noise a great deal and can lead to |
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320 | % many spurious sources (this depends, of course on the cube itself). |
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321 | % |
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322 | % The smoothing options have less parameters to consider: basically just |
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323 | % the size of the smoothing function or kernel. Spectrally smoothing |
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324 | % with a Hanning filter of width 3 (the smallest possible) is very |
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325 | % efficient at removing spurious one-channel objects that may result |
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326 | % just from statistical fluctuations of the noise. One may want to use |
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327 | % larger widths or kernels of larger size to look for features of a |
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328 | % particular scale in the cube. |
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329 | % |
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330 | % When it comes to searching, the FDR method produces more reliable |
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331 | % results than simple sigma-clipping, particularly in the absence of |
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332 | % reconstruction. However, it does not work in exactly the way one |
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333 | % would expect for a given value of \texttt{alpha}. For instance, |
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334 | % setting fairly liberal values of \texttt{alpha} (say, 0.1) will often |
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335 | % lead to a much smaller fraction of false detections (\ie much less |
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336 | % than 10\%). This is the effect of the merging algorithms, that combine |
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337 | % the sources after the detection stage, and reject detections not |
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338 | % meeting the minimum pixel or channel requirements. It is thus better |
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339 | % to aim for larger \texttt{alpha} values than those derived from a |
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340 | % straight conversion of the desired false detection rate. |
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341 | % |
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342 | % If the FDR method is not used, caution is required when choosing the |
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343 | % S/N cutoff. Typical cubes have very large numbers of pixels, so even |
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344 | % an apparently large cutoff will still result in a not-insignificant |
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345 | % number of detections simply due to random fluctuations of the noise |
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346 | % background. For instance, a $4\sigma$ threshold on a cube of Gaussian |
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347 | % noise of size $100\times100\times1024$ will result in $\sim340$ |
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348 | % single-pixel detections. This is where the minimum channel and pixel |
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349 | % requirements are important in rejecting spurious detections. |
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350 | % |
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351 | % %Finally, as \duchamp is still undergoing development, there are some |
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352 | % %elements that are not fully developed. In particular, it is not as |
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353 | % %clever as I would like at avoiding interference. The ability to place |
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354 | % %requirements on the minimum number of channels and pixels partially |
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355 | % %circumvents this problem, but work is being done to make \duchamp |
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356 | % %smarter at rejecting signals that are clearly (to a human eye at |
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357 | % %least) interference. See the following section for further |
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358 | % %improvements that are planned. |
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