Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 92, Issue 3, Pages -Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-022-01910-y
Keywords
Color image denosing; Beltrami minimization; Diffusion; Operator-splitting method
Categories
Funding
- National Natural Science Foundation of China [NSFC 12071345, 11701418]
- Major Science and Technology Project of Tianjin [18ZXRHSY00160]
- Recruitment Program of Global Young Expert
- NSF/RGC Grant [N-HKBU214-19]
- ANR/RGC Joint Research Scheme [A-HKBU203-19]
- [HKBU 12300819]
- [RC-FNRA-IG/19-20/SCI/01]
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The Beltrami framework is a successful technique for color image denosing that accurately models the coupling between color channels. This paper proposes an operator-splitting method to solve the optimization problems of the Beltrami regularization model, and demonstrates the efficiency and robustness of the algorithm through experiments.
The Beltrami framework is a successful technique for color image denosing by regarding color images as manifolds embedded in a five dimensional spatial-chromatic space. It can ideally model the coupling between the color channels rather than treating them as if they were independent. However, the resulting model with high nonlinearity makes the related optimization problems difficult to solve numerically. In this paper, we propose an operator-splitting method for a variant of the Beltrami regularization model. From the optimality conditions associated with the minimization of the Beltrami regularized functional, we derive an initial value problem (gradient flow). We solve the gradient flow problem by an operator-splitting scheme involving three fractional steps. All three subproblem solutions can be obtained in closed form or computed by one-step Newton's method. We demonstrate the efficiency and robustness of the proposed algorithm by conducting a series of experiments on real image denoising problems, where more than half of the computational time is saved compared to the existing augmented Lagrangian method (ALM) based algorithm for solving the Beltrami minimization model.
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