Large-Scale Inverse Problems in Imaging

Julianne Chung (), Sarah Knepper and James G. Nagy ()
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Julianne Chung: Virginia Tech
Sarah Knepper: Emory University
James G. Nagy: Emory University

A chapter in Handbook of Mathematical Methods in Imaging, 2015, pp 47-90 from Springer

Abstract: 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 model, a separable nonlinear model, 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.

Keywords: Inverse Problem; Singular Value Decomposition; Regularization Parameter; Point Spread Function; Tikhonov Regularization (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-1-4939-0790-8_2

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