What is it for? |
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| Spatio-Spectral Maximum Entropy Method (SSMEM) is a new attempt to extend traditional Maximum Entropy Method (MEM) to spectroscopic imaging so that maps at a wide range of frequencies can be reconstructed more consistently than single frequency mapping as it uses additional a priori information associated with global spectral property. The idea was first presented in a paper by Komm et al. (1997) and later a major upgrade has been made by Bong et al. (2004, 2005ab). | |
Background |
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| MEM is used in a variety of
fields, in particular, radio astronomy, where Fourier Transform imaging is
used. Based on information theory, MEM utilizes a priori knowledge (such
as uniformity and positivity of the map) in reconstructing spatial images in addition to the quantities
available from the direct measurement. Use of a priori information helps to reduce the ambiguity in imaging caused
by insufficient number of baselines (Wernecke & d'Addario 1977). In general scientists want to obtain spatial and spectral information altogether. This need has not been exploited by the existing astronomical instruments. It will, however, become more feasible with the newer generations of radio telescopes equipped with wideband receivers and backends. The existing techniques for handling multifrequencies (e.g., Multi-Frequency Synthesis, Sault & Conway 1999) assumes little change of source with frequency and would not fully address this issue. We therefore seek an algorithm that retains the spectral variation of intensity at a spatial point, and uses that information in determining the brightness temperature at the point to achieve wideband (extending over an octave) imaging spectroscopy. As an initial step in this regard, we develop an algorithm called Spatio-Spectral Maximum Entropy Method (SSMEM), that can extract the spectral, as well as spatial, information under the principle of MEM. |
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Algorithm |
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| We set the object function as: | |
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| In a more specific form, J is expressed as: | |
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| New in this approach is the term S called Spectral Entropy defined in analogy with traditional entropy H. | |
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where  . |
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| The next figure illustrates how we determine <T_{jk}> using a bilinear interpolation factor: | |
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| The maximization condition and the constraints are expressed as: | |
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| where | |
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| The main task in SSMEM is to solve (optimize) the above two sets of equations simultaneously. For efficient optimization, we have implemented two methods. One is the modified Newton-Raphson (NR) method (Cornwell & Evans 1985; Sault 1990), and the other is a more conservative, Conjugate Gradient (CG) Method (Press et al. 1992). | |
Sample results |
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Application |
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The SSMEM is most relevant to solar imaging spectroscopy, while they can also apply to other types of
Fourier-Transform imaging of astronomical objects at multiple
frequencies. At radio wavelengths, the SSMEM can be used with the currently available solar array, OVSA, and in future, the Frequency-Agile Solar Radiotelescope (FASR). The Enhanced Very Large Array (EVLA) data will also be amenable to use of SSMEM. Fourier-transform imaging is also employed in solar hard X-ray observations with, for instance, the Hard X-ray telescope onboard Yohkoh, and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). In radio imaging, we find the NR method better for computational efficiency. In the hard X-ray imaging with RHESSI, however, the synthesized beam varies depending on the position within maps, in which case we recommend the CG method instead. |
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What our collaborators say: |
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| "The RHESSI team is beginning to incorporate MEM mapping capability into their software using X-ray visibilities. The mapping program they use is the Maximum Entropy Method developed by NJIT workers for mapping OVSA radio visibilities. The RHESSI team is currently testing the NJIT MEM program on RHESSI hard X-ray flares and finds that is an improvement over their older MEM programs and that it compares favorably with Clean and Pixons." -Dr. Ed. Schmahl (NASA/GFSC, 2005). | |
| Biographical note | |
| Su-Chan Bong works in Korea Astronomy and Space Science Institute (KASI) as post-doctoral research fellow. The SSMEM was mainly developed as part of his thesis work in Seoul National University, 2004. | |
References |
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| Bong, S.-C., Lee, J., Gary, D. E. Gary, & Yun, H. S. 2005 | |
| ApJ, in press | |
| Bong, S.-C., Lee, J., Gary, D. E. Gary, Yun, H. S., & Chae, J. 2005 | |
| JKAS, submitted | |
| Bong, S.-C. 2004 | |
| Ph.D. thesis, Seoul National University, Korea | |
| Bong, S.-C.; Lee, J., Gary, Dale E. Yun, H. S. 2003 | |
| JKAS, 36S, 29 | |
| Cornwell, T. J., & Evans, K. F. 1985 | |
| Astronomy & Astrophysics, 143, 77 | |
| Komm, R. W., Hurford, G. J., & Gary, D. E. 1997 | |
| Astronomy & Astrophysics Supplement, 122, 181 | |
| Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992 | |
| Numerical recipes in C: The Art of Scientific Computing(2nd ed.; Cambridge: Cambridge Univ. Press), P. 420 | |
| Sault, R. J. 1990, ApJ, 354, L61 | |
| Sault, R. J., & Conway, J. E. 1999 | |
| in ASP Conf. Ser. 180, Synthesis Imaging in Radio Astronomy II, ed. G. B. Taylor, C. L.Carilli, & R. A. Perley (San Francisco: ASP), 419 | |
| Wernecke, S. J., & D'Addario, L. R. 1977 | |
| IEEE Trans. Comp., C-26, 351 | |
| White, S. M., Lee, J., Aschwanden, M. J., & Bastian, T. S. 2003 | |
| in Proc. of the SPIE, 4853, Innovative Telescopes and Instrumentation for Solar Astrophysics, ed. S. L. Keil, & S. V.Avakyan (SPIE), 531 | |
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| Last modified: 2005 Nov. 15 J. Lee | |