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**Split Bregman iteration algorithm for total bounded variation regularization based image deblurring.**
*(English)*
Zbl 1202.94062

A novel total bounded variation regularization based image deblurring model is presented in the paper. The necessary definitions and preliminaries about the proposed model are described. A brief overview of some related iterative algorithms is given. Existence and uniqueness of the proposed extended split Bregman iteration is proven. Based on this, a rigorous convergence analysis of the corresponded iterative algorithm is provided. Numerical experiments intended for demonstrating the proposed method are accomplished. Three numerical results are presented to illustrate the efficiency and feasibility of the proposed algorithm. It is compared with the standard total variation based regularization scheme of L. I. Rudin, S. Osher and E. Fatemi [Physica D 60, No. 1–4, 259–268 (1992; Zbl 0780.49028)] (the ROF model). The computations are performed in MATLAB. The obtained results are very promising particularly from the preserved details point of view compared with the standard scheme of the ROF method. It is believed that the proposed model and algorithm can be extended to further application in image processing and computer vision.

Reviewer: Tzvetan Semerdjiev (Sofia)

### MSC:

94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |

### Citations:

Zbl 0780.49028
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\textit{X. Liu} and \textit{L. Huang}, J. Math. Anal. Appl. 372, No. 2, 486--495 (2010; Zbl 1202.94062)

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### References:

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