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Convex Optimization for Image Reconstruction

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Abstract

Convex optimization is a particular class of mathematical tool in decision sciences and in analyzing physical systems for finding a point that maximizes/minimizes an objective function (subjected to equality constraints and/or inequality constraints) through iterative computations. In this regard, recent developments in the mathematics and computational fields have sparked and positioned convex optimization as one of the most powerful tools to formulate and solve image inverse problems. This chapter briefly introduces state-of-the-art convex optimization methods for such reconstruction problems and presents the most successful approaches and their interconnections. Section 3.1 summarizes the basic concepts of convex optimization, focusing on the convexity conditions; Section 3.2 introduces the principal mathematical optimization tools for image/signal processing, focusing on the role of convex optimization. Section 3.3 discusses a variety of conventional convex optimization-based reconstruction algorithms used in the image processing community. The scope of these mathematical concepts, algorithms, and their applications are extended as needed in the remainder of the book.

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Acknowledgments

This chapter was supported by the Sistema general de regalías Colombia under Grant BPIN 2020000100415, with UIS code 8933.

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Authors and Affiliations

  1. Universidad Industrial de Santander, Computer Science Department, Bucaramanga, Santander, Colombia

    Henry Arguello

  2. Universidad Industrial de Santander, Department of Physics, Bucaramanga, Santander, Colombia

    Miguel Marquez

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Correspondence to Henry Arguello .

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  1. Laboratory of Applied Computational Imaging, Institut National de la Recherche Scientifique Université du Québec, Varennes, QC, Canada

    **yang Liang

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Arguello, H., Marquez, M. (2024). Convex Optimization for Image Reconstruction. In: Liang, J. (eds) Coded Optical Imaging. Springer, Cham. https://doi.org/10.1007/978-3-031-39062-3_3

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