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Microlocal Analysis of Some Synthetic Aperture Radar Imaging Problems

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Mathematical Models, Methods and Applications

Part of the book series: Industrial and Applied Mathematics ((INAMA))

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Abstract

In this article, we analyze the microlocal properties of the linearized forward scattering operator \({\mathcal{F}},\) which arises in synthetic aperture radar imaging. A frequently applied imaging technique is to study the normal operator \({\mathcal{F}^{\ast} \mathcal{F}}\) (\({\mathcal{F}^{\ast}}\) is the L 2 adjoint of \({\mathcal{F}}\)). However, such an imaging technique introduces artifacts in the image. We study the structure of these artifacts.

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Acknowledgments

The author thanks Prof. Abul Hasan Siddiqi, Prof. Pammy Manchanda and the organizers for the invitation to give a talk in the 11th Annual Conference of the Indian Society of Industrial and Applied Mathematics titled, “Emerging Mathematical Methods, Models and Algorithms for Science and Technology” at Gautam Buddha University (GBU) on December 15 and 16, 2012, commemorating the 125th birth year of Srinivasa Ramanujan, and for the warm hospitality during his stay on GBU campus. He also thanks Prof. Siddiqi for inviting to contribute an article in the proceedings. The material here is a slightly expanded version of the talk given at this conference.

The author was partially supported by NSF Grant DMS 1109417.

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Authors and Affiliations

  1. Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore, India

    Venkateswaran P. Krishnan

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  1. Venkateswaran P. Krishnan
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Correspondence to Venkateswaran P. Krishnan .

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Editors and Affiliations

  1. School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, India

    Abul Hasan Siddiqi

  2. Guru Nanak Dev University, Amritsar, Punjab, India

    Pammy Manchanda

  3. University, Guru Gobind Singh Indraprastha, Dwarka, India

    Rashmi Bhardwaj

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Krishnan, V.P. (2015). Microlocal Analysis of Some Synthetic Aperture Radar Imaging Problems. In: Siddiqi, A., Manchanda, P., Bhardwaj, R. (eds) Mathematical Models, Methods and Applications. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-287-973-8_4

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