Fast Proximal Gradient Methods for Nonsmooth Convex Optimization for Tomographic Image Reconstruction

The Fast Proximal Gradient Method (FPGM) and the Monotone FPGM (MFPGM) for minimization of nonsmooth convex functions are introduced and applied to tomographic image reconstruction. Convergence properties of the sequence of objective function values are derived, including a O 1 / k 2 non-asymptotic...

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Vydáno v:Sensing and imaging Ročník 21; číslo 1
Hlavní autoři: Helou, Elias S., Zibetti, Marcelo V. W., Herman, Gabor T.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2020
Springer Nature B.V
Témata:
Algorithms
Computational geometry
Computed tomography
Convergence
Convex analysis
Convexity
Electrical Engineering
Engineering
Experimentation
Image reconstruction
Imaging
Microwaves
Optimization
Original Paper
Radiology
RF and Optical Engineering
Computerized tomography imaging
Iterative algorithms
Convex optimization
Proximal gradient methods
ISSN:1557-2064, 1557-2072
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Shrnutí:The Fast Proximal Gradient Method (FPGM) and the Monotone FPGM (MFPGM) for minimization of nonsmooth convex functions are introduced and applied to tomographic image reconstruction. Convergence properties of the sequence of objective function values are derived, including a O 1 / k 2 non-asymptotic bound. The presented theory broadens current knowledge and explains the convergence behavior of certain methods that are known to present good practical performance. Numerical experimentation involving computerized tomography image reconstruction shows the methods to be competitive in practical scenarios. Experimental comparison with Algebraic Reconstruction Techniques are performed uncovering certain behaviors of accelerated Proximal Gradient algorithms that apparently have not yet been noticed when these are applied to tomographic image reconstruction.
Bibliografie:ObjectType-Article-1
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ISSN:1557-2064
1557-2072
DOI:10.1007/s11220-020-00309-z