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Signal and image restoration using shock filters and anisotropic diffusion. (English) Zbl 0804.65130
Summary: The authors define a new class of filters for noise elimination and edge enhancement by using shock filters and anisotropic diffusion. Some nonlinear partial differential equations used as models for these filters are studied. The authors develop recursive and unconditional stable schemes which drastically reduce the computational effort of the algorithms. A new fast recursive approach to linear Gaussian filters is also shown by using the heat equation.
MSC:
65Z05Applications of numerical analysis to physics
65M06Finite difference methods (IVP of PDE)
35Q80Appl. of PDE in areas other than physics (MSC2000)
35L67Shocks and singularities
94A12Signal theory (characterization, reconstruction, filtering, etc.)