A new step size rule for the superiorization method and its application in computerized tomography

In this paper, we consider a regularized least squares problem subject to convex constraints. Our algorithm is based on the superiorization technique, equipped with a new step size rule which uses subgradient projections. The superiorization method is a two-step method where one step reduces the val...

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Vydáno v:Numerical algorithms Ročník 90; číslo 3; s. 1253 - 1277
Hlavní autoři: Nikazad, T., Abbasi, M., Afzalipour, L., Elfving, T.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.07.2022
Springer Nature B.V
Témata:
Algebra
Algorithms
Computed tomography
Computer Science
Conjugate gradient method
Convergence
Iterative methods
Least squares method
Numeric Computing
Numerical Analysis
Original Paper
Regularization
Theory of Computation
Tomography
Strictly quasi-nonexpansive operator
Convex feasibility problem
Computed tomography
65F10
Convex optimization
Sequential block method
Perturbation resilient iterative method
47J25
Superiorization
47H14
ISSN:1017-1398, 1572-9265, 1572-9265
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Shrnutí:In this paper, we consider a regularized least squares problem subject to convex constraints. Our algorithm is based on the superiorization technique, equipped with a new step size rule which uses subgradient projections. The superiorization method is a two-step method where one step reduces the value of the penalty term and the other step reduces the residual of the underlying linear system (using an algorithmic operator T ). For the new step size rule, we present a convergence analysis for the case when T belongs to a large subclass of strictly quasi-nonexpansive operators. To examine our algorithm numerically, we consider box constraints and use the total variation (TV) functional as a regularization term. The specific test cases are chosen from computed tomography using both noisy and noiseless data. We compare our algorithm with previously used parameters in superiorization. The T operator is based on sequential block iteration (for which our convergence analysis is valid), but we also use the conjugate gradient method (without theoretical support). Finally, we compare with the well-known “fast iterative shrinkage-thresholding algorithm” (FISTA). The numerical results demonstrate that our new step size rule improves previous step size rules for the superiorization methodology and is competitive with, and in several instances behaves better than, the other methods.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:1017-1398
1572-9265
1572-9265
DOI:10.1007/s11075-021-01229-z