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Preliminaries

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2098)

Abstract

This chapter reviews some mathematical and statistical concepts essential for understanding multistatic imaging principles. We first review commonly used special functions, function spaces, and an integral transform: the Fourier transform. We then collect basic facts about the Moore-Penrose generalized inverse, singular value decomposition, and compact operators. The theory of regularization of ill-posed inverse problems is briefly discussed. Then we introduce useful probabilistic tools for imaging in the presence of noise. In particular, we review results on the statistics of the singular values of a random matrix. Such results will be of help to us when dealing with inclusion detection tests. Finally, we examine image characteristics with respect to various data acquisition and processing schemes. We focus specifically on issues related to image resolution, signal-to-noise ratio, and image artifacts.

Keywords

  • Probability Density Function
  • Singular Value Decomposition
  • Point Spread Function
  • Compact Operator
  • Random Matrix

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2013 Springer International Publishing Switzerland

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Ammari, H. et al. (2013). Preliminaries. In: Mathematical and Statistical Methods for Multistatic Imaging. Lecture Notes in Mathematics, vol 2098. Springer, Cham. https://doi.org/10.1007/978-3-319-02585-8_1

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