Ultrasound Image Filtering Using Partial Differential Equations The speckle reducing anisotropic diffusion (SRAD) filter is extensively used to process the ultrasound image. However, in the image processed by SRAD filter, there could be slab effects, blurred weak boundaries, and lost details in the homogeneous region, and the iterative process cannot be terminated adaptively. To solve these problems, an improved diffusion coefficient is proposed, and the adaptive iterative termination condition is added. The result of the experiments shows that the optimization algorithm can efficiently eliminate the plate effect in the homogenous region and has a better visual effect than the traditional SRAD. And according to the criteria for quantifying algorithm performance, the optimization algorithm could not only well remove the speckle but also is more suitable for image segmentation than SRAD.

Efficient and consistent recursive filtering of images with reflective extension Recursive filters are commonly used in scale space construction for their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of reflectively extended images for filters with symmetric denominator. We begin with an analysis of reflective extensions and their effect on nonrecursive filtering operators. Based on the nonrecursive case, we derive a formulation of recursive filtering on reflective domains as a linear but timevarying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring the same order of computation as the standard recursive filtering. We give experimental evidence to verify these claims.