AI Article Synopsis
- This paper introduces a mixed finite element method for linear multivariate splines enhanced by a Laplacian penalty.
- The approach employs biorthogonal systems, which simplifies the finite element scheme for improved efficiency.
- Additionally, the method is expanded to handle nonlinear cases using a split Bregman iteration scheme to address associated nonlinear equations and is applied to reduce Gaussian and impulsive noise in test images.
Article Abstract
We consider a mixed finite element method for a linear multivariate spline using the Laplacian penalty. Our discretisation is based on biorthogonal systems leading to a very simple and efficient finite element scheme. We also extend our approach to a nonlinear case and describe a split Bregman iteration scheme for the resulting nonlinear equations. We apply our numerical schemes to remove the mixture of Gaussian and impulsive noise for some test images.•This paper presents a method of discretising a multivariate spline using a finite element method.•The method uses a biorthogonal system to achieve an efficient finite element method.•The method is extended to cover a discretisation scheme for a nonlinear case, including an adaptation of the split Bregman method for the nonlinear case.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9791608 | PMC |
| http://dx.doi.org/10.1016/j.mex.2022.101962 | DOI Listing |
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