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On global randomized block Kaczmarz method for image reconstruction

  • Received: 22 December 2021 Revised: 10 March 2022 Accepted: 10 March 2022 Published: 21 March 2022
  • Image reconstruction represents an important technique applied in various fields such as medicine, biology, materials science, nondestructive testing, and so forth. In this paper, we transform the problem of image reconstruction into the problem of solving linear systems with multiple right-hand sides. Based on the idea of K-means clustering, we propose the global randomized block Kaczmarz method, so as to solve the problem of the linear systems with multiple right-hand sides effectively and use this method to image reconstruction. Theoretical analysis proves the convergence of this method, and the simulation results demonstrate the performance of this method in image reconstruction.

    Citation: Ranran Li, Hao Liu. On global randomized block Kaczmarz method for image reconstruction[J]. Electronic Research Archive, 2022, 30(4): 1442-1453. doi: 10.3934/era.2022075

    Related Papers:

  • Image reconstruction represents an important technique applied in various fields such as medicine, biology, materials science, nondestructive testing, and so forth. In this paper, we transform the problem of image reconstruction into the problem of solving linear systems with multiple right-hand sides. Based on the idea of K-means clustering, we propose the global randomized block Kaczmarz method, so as to solve the problem of the linear systems with multiple right-hand sides effectively and use this method to image reconstruction. Theoretical analysis proves the convergence of this method, and the simulation results demonstrate the performance of this method in image reconstruction.



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