Noise Removal Using Edge-Preserving Fourth-Order Partial Differential Equations

Over the last decade, partial differential equations (PDEs) have been justified as effective tools for image smoothing; they are able to achieve a good trade-off between noise removal and edge-preserving. Among various methods, the second-order PDEs provide better results than other conventional methods, but staircasing effect can always be observed; the fourth-order PDEs can alleviate this staircasing effect, but its edge-preserving ability is not satisfactory. In this paper, a class of novel fourth-order PDEs are proposed, which seek to approximate the noisy image with an almost harmonic image and simultaneously preserve the edges. The properties of the proposed method are demonstrated with numerical examples and compared with that of a popular one.