Two-level method for the total fractional-order variation model in image deblurring problem. (English) Zbl 1451.94008
Summary: Image deblurring with total fractional-order variation model is used to improve the quality of the deblurred images. This model is very efficient in preserving edges and removing staircase effect. However, the regularization matrix associated with the total fractional-order model is dense which complicate developing an efficient numerical algorithm. In this research work, we present an efficient and robust Two-Level method to overcome the dense problem. The Two-Level method started by reducing the problem to one small non-linear system with dense regularization matrix (Level-I) and one less expensive large linear system with sparse regularization matrix (Level-II). The derivation of the optimal regularization parameter of Level-II is studied and formula is presented. Numerical experiments on several images are also provided to demonstrate the efficiency of the Two-Level method.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 65F08 | Preconditioners for iterative methods |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
Keywords:
image deblurring; Krylov subspace methods; total fractional-order variation model; two-level methodReferences:
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