[3] | 1 | \documentclass[11pt]{article} |
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| 27 | }% |
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| 28 | }% |
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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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