[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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[1011] | 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 | Section~\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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[1023] | 90 | \secB{Timing considerations} |
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[1011] | 91 | |
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[1023] | 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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[993] | 99 | |
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[1023] | 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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[1011] | 112 | |
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[1023] | 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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[158] | 121 | |
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[1023] | 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 the 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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[285] | 131 | |
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| 132 | |
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[1023] | 133 | \secB{Should there be preprocessing?} |
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[158] | 134 | |
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[1023] | 135 | Why do preprocessing? Effect on completeness and reliability. Cite |
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| 136 | results from MNRAS paper and given basic summary of what each does. |
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[158] | 137 | |
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[1023] | 138 | \secB{Reconstruction considerations} |
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[1011] | 139 | |
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[1023] | 140 | Several things: |
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| 141 | \begin{itemize} |
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| 142 | \item Beam effects and residual noise |
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| 143 | \item Memory and time recap |
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| 144 | \item Details on how it works. |
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| 145 | \item Effect of subsectioning |
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| 146 | \end{itemize} |
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[292] | 147 | |
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[1023] | 148 | \secB{Smoothing considerations} |
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[158] | 149 | |
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[1023] | 150 | Anything here? Edge effects? |
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[964] | 151 | |
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[1023] | 152 | \secB{Threshold method} |
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[158] | 153 | |
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| 154 | When it comes to searching, the FDR method produces more reliable |
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| 155 | results than simple sigma-clipping, particularly in the absence of |
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| 156 | reconstruction. However, it does not work in exactly the way one |
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| 157 | would expect for a given value of \texttt{alpha}. For instance, |
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| 158 | setting fairly liberal values of \texttt{alpha} (say, 0.1) will often |
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| 159 | lead to a much smaller fraction of false detections (\ie much less |
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| 160 | than 10\%). This is the effect of the merging algorithms, that combine |
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| 161 | the sources after the detection stage, and reject detections not |
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| 162 | meeting the minimum pixel or channel requirements. It is thus better |
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| 163 | to aim for larger \texttt{alpha} values than those derived from a |
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| 164 | straight conversion of the desired false detection rate. |
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| 165 | |
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[292] | 166 | If the FDR method is not used, caution is required when choosing the |
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| 167 | S/N cutoff. Typical cubes have very large numbers of pixels, so even |
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| 168 | an apparently large cutoff will still result in a not-insignificant |
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| 169 | number of detections simply due to random fluctuations of the noise |
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| 170 | background. For instance, a $4\sigma$ threshold on a cube of Gaussian |
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| 171 | noise of size $100\times100\times1024$ will result in $\sim340$ |
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[964] | 172 | single-pixel detections. This is where the minimum channel and pixel |
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| 173 | requirements are important in rejecting spurious detections. |
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[292] | 174 | |
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[1023] | 175 | |
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| 176 | % \secB{Preprocessing} |
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| 177 | % |
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| 178 | % \secC{Should I do any preprocessing?} |
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| 179 | % |
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| 180 | % The main choice is whether to alter the cube to try and enhance the |
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| 181 | % detectability of objects, by either smoothing or reconstructing via |
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| 182 | % the \atrous method. The main benefits of both methods are the marked |
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| 183 | % reduction in the noise level, leading to regularly-shaped detections, |
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| 184 | % and good reliability for faint sources. |
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| 185 | % |
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| 186 | % The main drawback with the \atrous method is the long execution time: |
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| 187 | % to reconstruct a $170\times160\times1024$ (\hipass) cube often |
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| 188 | % requires three iterations and takes about 20-25 minutes to run |
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| 189 | % completely. Note that this is for the more complete three-dimensional |
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| 190 | % reconstruction: using \texttt{reconDim = 1} makes the reconstruction |
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| 191 | % quicker (the full program then takes less than 5 minutes), but it is |
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| 192 | % still the largest part of the time. |
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| 193 | % |
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| 194 | % The smoothing procedure is computationally simpler, and thus quicker, |
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| 195 | % than the reconstruction. The spectral Hanning method adds only a very |
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| 196 | % small overhead on the execution, and the spatial Gaussian method, |
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| 197 | % while taking longer, will be done (for the above example) in less than |
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| 198 | % 2 minutes. Note that these times will depend on the size of the |
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| 199 | % filter/kernel used: a larger filter means more calculations. |
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| 200 | % |
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| 201 | % The searching part of the procedure is much quicker: searching an |
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| 202 | % un-reconstructed cube leads to execution times of less than a |
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| 203 | % minute. Alternatively, using the ability to read in previously-saved |
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| 204 | % reconstructed arrays makes running the reconstruction more than once a |
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| 205 | % more feasible prospect. |
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| 206 | % |
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| 207 | % On the positive side, the shape of the detections in a cube that has |
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| 208 | % been reconstructed or smoothed will be much more regular and smooth -- |
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| 209 | % the ragged edges that objects in the raw cube possess are smoothed by |
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| 210 | % the removal of most of the noise. This enables better determination of |
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| 211 | % the shapes and characteristics of objects. |
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| 212 | % |
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| 213 | % \secC{Reconstruction vs Smoothing} |
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| 214 | % |
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| 215 | % While the time overhead is larger for the reconstruction case, it will |
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| 216 | % potentially provide a better recovery of real sources than the |
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| 217 | % smoothing case. This is because it probes the full range of scales |
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| 218 | % present in the cube (or spectral domain), rather than the specific |
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| 219 | % scale determined by the Hanning filter or Gaussian kernel used in the |
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| 220 | % smoothing. |
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| 221 | % |
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| 222 | % When considering the reconstruction method, note that the 2D |
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| 223 | % reconstruction (\texttt{reconDim = 2}) can be susceptible to edge |
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| 224 | % effects. If the valid area in the cube (\ie the part that is not |
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| 225 | % BLANK) has non-rectangular edges, the convolution can produce |
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| 226 | % artefacts in the reconstruction that mimic the edges and can lead |
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| 227 | % (depending on the selection threshold) to some spurious |
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| 228 | % sources. Caution is advised with such data -- the user is advised to |
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| 229 | % check carefully the reconstructed cube for the presence of such |
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| 230 | % artefacts. |
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| 231 | % |
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| 232 | % A more important effect that can be important for 2D reconstructions |
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| 233 | % is the fact that the pixels in the spatial domain typically exhibit |
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| 234 | % some correlation due to the beam. Since each channel is reconstructed |
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| 235 | % independently, beam-sized noise fluctuations can rise above the |
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| 236 | % reconstruction threshold more frequency than in the 1D case, providing |
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| 237 | % a greater number of spurious single-channel spikes in a given |
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| 238 | % reconstructed spectrum. This effect will also be present in 3D |
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| 239 | % reconstructions, although to a lesser degree since information in the |
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| 240 | % spectral direction is also taken into account. |
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| 241 | % |
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| 242 | % If one chooses the reconstruction method, a further decision is |
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| 243 | % required on the signal-to-noise cutoff used in determining acceptable |
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| 244 | % wavelet coefficients. A larger value will remove more noise from the |
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| 245 | % cube, at the expense of losing fainter sources, while a smaller value |
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| 246 | % will include more noise, which may produce spurious detections, but |
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| 247 | % will be more sensitive to faint sources. Values of less than about |
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| 248 | % $3\sigma$ tend to not reduce the noise a great deal and can lead to |
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| 249 | % many spurious sources (this depends, of course on the cube itself). |
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| 250 | % |
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| 251 | % The smoothing options have less parameters to consider: basically just |
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| 252 | % the size of the smoothing function or kernel. Spectrally smoothing |
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| 253 | % with a Hanning filter of width 3 (the smallest possible) is very |
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| 254 | % efficient at removing spurious one-channel objects that may result |
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| 255 | % just from statistical fluctuations of the noise. One may want to use |
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| 256 | % larger widths or kernels of larger size to look for features of a |
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| 257 | % particular scale in the cube. |
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| 258 | % |
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| 259 | % When it comes to searching, the FDR method produces more reliable |
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| 260 | % results than simple sigma-clipping, particularly in the absence of |
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| 261 | % reconstruction. However, it does not work in exactly the way one |
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| 262 | % would expect for a given value of \texttt{alpha}. For instance, |
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| 263 | % setting fairly liberal values of \texttt{alpha} (say, 0.1) will often |
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| 264 | % lead to a much smaller fraction of false detections (\ie much less |
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| 265 | % than 10\%). This is the effect of the merging algorithms, that combine |
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| 266 | % the sources after the detection stage, and reject detections not |
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| 267 | % meeting the minimum pixel or channel requirements. It is thus better |
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| 268 | % to aim for larger \texttt{alpha} values than those derived from a |
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| 269 | % straight conversion of the desired false detection rate. |
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| 270 | % |
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| 271 | % If the FDR method is not used, caution is required when choosing the |
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| 272 | % S/N cutoff. Typical cubes have very large numbers of pixels, so even |
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| 273 | % an apparently large cutoff will still result in a not-insignificant |
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| 274 | % number of detections simply due to random fluctuations of the noise |
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| 275 | % background. For instance, a $4\sigma$ threshold on a cube of Gaussian |
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| 276 | % noise of size $100\times100\times1024$ will result in $\sim340$ |
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| 277 | % single-pixel detections. This is where the minimum channel and pixel |
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| 278 | % requirements are important in rejecting spurious detections. |
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| 279 | % |
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| 280 | % %Finally, as \duchamp is still undergoing development, there are some |
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| 281 | % %elements that are not fully developed. In particular, it is not as |
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| 282 | % %clever as I would like at avoiding interference. The ability to place |
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| 283 | % %requirements on the minimum number of channels and pixels partially |
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| 284 | % %circumvents this problem, but work is being done to make \duchamp |
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| 285 | % %smarter at rejecting signals that are clearly (to a human eye at |
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| 286 | % %least) interference. See the following section for further |
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| 287 | % %improvements that are planned. |
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