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Large-Scale Inverse Problems in Imaging

In: Handbook of Mathematical Methods in Imaging

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  • Julianne Chung
  • Sarah Knepper
  • James G. Nagy

Abstract

Large-scale inverse problems arise in a variety of significant applications in image processing, and efficient regularization methods are needed to compute meaningful solutions. This chapter surveys three common mathematical models including a linear, a separable nonlinear, and a general nonlinear model. Techniques for regularization and large-scale implementations are considered, with particular focus on algorithms and computations that can exploit structure in the problem. Examples from image deconvolution, multi-frame blind deconvolution, and tomosynthesis illustrate the potential of these algorithms. Much progress has been made in the field of large-scale inverse problems, but many challenges still remain for future research.

Suggested Citation

  • Julianne Chung & Sarah Knepper & James G. Nagy, 2011. "Large-Scale Inverse Problems in Imaging," Springer Books, in: Otmar Scherzer (ed.), Handbook of Mathematical Methods in Imaging, chapter 2, pages 43-86, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-92920-0_2
    DOI: 10.1007/978-0-387-92920-0_2
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