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On Randomized Sampling Kaczmarz Method with Application in Compressed Sensing
Joint Authors
Sun, Mei-Lan
Tang, Peng-Fei
Gu, Chuanqing
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-03-30
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We propose a randomized sampling Kaczmarz algorithm for the solution of very large systems of linear equations by introducing a maximal sampling probability control criterion, which is aimed at grasping the largest entry of the absolute sampling residual vector at each iteration.
This new method differs from the greedy randomized Kaczmarz algorithm, which needs not to compute the residual vector of the whole linear system to determine the working rows.
Numerical experiments show that the proposed algorithm has the most significant effect when the selected row number, i.e, the size of samples, is equal to the logarithm of all rows.
Finally, we extend the randomized sampling Kaczmarz to signal reconstruction problems in compressed sensing.
Signal experiments show that the new extended algorithm is more effective than the randomized sparse Kaczmarz method for online compressed sensing.
American Psychological Association (APA)
Sun, Mei-Lan& Gu, Chuanqing& Tang, Peng-Fei. 2020. On Randomized Sampling Kaczmarz Method with Application in Compressed Sensing. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1198014
Modern Language Association (MLA)
Sun, Mei-Lan…[et al.]. On Randomized Sampling Kaczmarz Method with Application in Compressed Sensing. Mathematical Problems in Engineering No. 2020 (2020), pp.1-11.
https://search.emarefa.net/detail/BIM-1198014
American Medical Association (AMA)
Sun, Mei-Lan& Gu, Chuanqing& Tang, Peng-Fei. On Randomized Sampling Kaczmarz Method with Application in Compressed Sensing. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1198014
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1198014