A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the absolute value of the Laplacian of the image intensity function. Since the Laplacian of an image at a pixel is zero if the image is planar in i...

Data smoothing algorithms are commonly applied to reduce the level of noise and eliminate the weak textures contained in digital images. Anisotropic diffusion algorithms form a distinct category of noise removal approaches that implement the smoothing process locally in agreement with image features such as edges that are typically determined by applying diverse partial differential equation (P...

This paper presents an approach for reducing speckle in three dimensional (3D) ultrasound images. A 2D speckle reduction technique, speckle reducing anisotropic diffusion (SRAD), is explored and extended to 3D. 3D SRAD is advantageous in that, like 2D SRAD, it keeps the advantages of the conventional anisotropic diffusion and the traditional speckle reducing filter, the Lee filter, by exploitin...

Images secured from an astronomical telescope usually suffer from blur and from interference that scientists refer to as ‘‘noise’’. Therefore, good image restoration technique has become an important tool in astronomical observation. In this paper, we propose a modified anisotropic diffusion scheme to tackle the problem of image restoration in astronomy, especially in the case of nebula images....