Adaptive smoothing and its application to the inversion of the Crab synchrotron spectrum

Details Adaptive smoothing and its application to the inversion of the Crab synchrotron spectrum Adaptive smoothing and its application to the inversion of the Crab synchrotron spectrum

Dec 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990a%26a...240..209t&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 240, no. 1, Dec. 1990, p. 209-215. Research supported by SERC.

Astronomy and Astrophysics

Astrophysics

6

Adaptive Filters, Crab Nebula, Data Smoothing, Image Processing, Synchrotron Radiation, Electron Energy, Kernel Functions, Spectral Energy Distribution

Scientific paper

The smoothing properties of the regularization constraints are examined in the context of integral inversion problems with large dynamic ranges. It is shown that commonly used regularization techniques tend to produce uneven amounts of smoothing on the source function, with the effect that some parts of the source function are oversmoothed while others may still exhibit high-frequency oscillations. Consequently, the reconstructed source function may be heavily biased at some points and totally unstable at others. It is shown that, by using a suitable prior form of the source function to transform the kernel, the dynamic range of the source function to be recovered can be reduced, thus reducing the problem of distortion by uniform smoothing methods while retaining the computational advantages of using a quadratic prior. The technique is applied to the problem of inverting the Crab synchrotron spectrum, obtaining more structure in the center of the spectrum than that obtained by Craig et al. (1985).

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