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27 | }% |
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29 | {\end{list}} |
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30 | |
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31 | \title{The ``noiseless reconstruction'' of astronomical data cubes |
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32 | using the multi-scale {\it \`a trous} wavelet technique.} |
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33 | |
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34 | \author{Matthew Whiting\\Australia Telescope National Facility\\CSIRO} |
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35 | |
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36 | \date{November 2005} |
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37 | |
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38 | \begin{document} |
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39 | |
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40 | \maketitle |
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41 | |
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42 | \begin{abstract} |
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43 | We describe a technique to reconstruct a three-dimensional FITS data |
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44 | cube using multi-scale wavelet decomposition. The technique provides a |
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45 | marked reduction in the noise level of the cube, while retaining |
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46 | objects, providing an excellent basis for a source-finding algorithm. |
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47 | \end{abstract} |
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48 | |
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49 | \section{Background} |
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50 | |
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51 | An important step in most astronomical data analysis that involves |
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52 | multi-dimensional imaging or spectroscopic data is the detection of |
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53 | sources. Often, astronomical sources (be they stars, galaxies, masers |
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54 | or otherwise) are faint and of a strength close to the noise or |
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55 | background of the image. Any procedure that could reduce this |
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56 | statistical background without removing the real features would be a |
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57 | great aid in detecting such sources. |
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58 | |
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59 | This is of great interest for large-scale surveys: large-scale here |
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60 | meaning both the size of data produced as well as the area of the sky |
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61 | they cover. The data rate seen in many current and planned surveys |
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62 | necessitates a largely automated pipeline reduction process, with |
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63 | minimal input from a user***. An object-detection (and |
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64 | characterisation) process is the logical next step (particularly with |
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65 | a view to producing source catalogues and the like), and such a |
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66 | process will need to be as sensitive as possible. This means beating |
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67 | the noise level in some way. |
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68 | |
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69 | *** MATCHED FILTERS *** |
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70 | |
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71 | *** SMOOTHING *** |
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72 | |
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73 | *** WAVELETS *** |
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74 | |
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75 | \section{Wavelet decomposition} |
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76 | |
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77 | The technique we describe here relies on the properties of |
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78 | wavelets. These are localised functions that are described by two |
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79 | parameters, location (where the wavelet is operating) and scale (what |
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80 | range of values it operates on). An example of a wavelet is shown in |
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81 | Fig.~\ref{fig-wavelet}. |
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82 | |
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83 | \begin{figure} |
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84 | \vspace{7.0cm} |
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85 | \caption{An example of a wavelet function.} |
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86 | \label{fig-wavelet} |
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87 | \end{figure} |
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88 | |
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89 | |
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90 | |
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91 | \section{Implementation} |
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92 | |
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93 | \subsection{Method} |
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94 | |
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95 | \subsection{Edge effects} |
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96 | |
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97 | |
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98 | \section{Results} |
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99 | |
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100 | \section{Applications of the technique} |
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101 | |
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102 | \section{Conclusions} |
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103 | |
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104 | |
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105 | \end{document} |
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