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Tikhonov Regularization for Gravitational Lensing Research

In: Optimization and Regularization for Computational Inverse Problems and Applications

Author

Listed:
  • Boris Artamonov

    (Sternberg Astronomical Institute of Moscow State University)

  • Ekaterina Koptelova

    (Sternberg Astronomical Institute of Moscow State University)

  • Elena Shimanovskaya

    (Sternberg Astronomical Institute of Moscow State University)

  • Anatoly G. Yagola

    (Lomonosov Moscow State University, Department of Mathematics, Faculty of Physics)

Abstract

The gravitational lensing phenomenon can provide us with the information about luminous and dark matter in our Universe. But robust and effective tools are needed to extract that valuable information from observations. In this chapter, two inverse problems arising in gravitational lensing research are considered. Both problems are ill-posed, so regularization is needed. The first problem is the one of image reconstruction. Based on the Tikhonov regularization approach, several modifications of the regularizing algorithm, taking account of specific properties of gravitational lens systems, are proposed. The numerical results show that incorporation of all available a priori information allows reconstructing images of gravitational lens systems quite well. Furthermore, the algorithm decomposes the images into two parts — point sources and smooth background, that is needed for further investigations. The second problem concerns reconstruction of a distant quasar light distribution based on observations of microlensing events. In this case, a gravitational lens system as a gravitational telescope and the Tikhonov regularization method as a tool allow getting valuable information about the distant quasar unresolved by an instrument.

Suggested Citation

  • Boris Artamonov & Ekaterina Koptelova & Elena Shimanovskaya & Anatoly G. Yagola, 2010. "Tikhonov Regularization for Gravitational Lensing Research," Springer Books, in: Yanfei Wang & Changchun Yang & Anatoly G. Yagola (ed.), Optimization and Regularization for Computational Inverse Problems and Applications, chapter 0, pages 327-347, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-13742-6_14
    DOI: 10.1007/978-3-642-13742-6_14
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