Robust edge-directed interpolation of magnetic resonance images

Image interpolation is intrinsically a severely under-determined inverse problem. Traditional non-adaptive interpolation methods do not account for local image statistics around the edges of image structures. In practice, this results in artifacts such as jagged edges, blurring and/or edge halos. To overcome this shortcoming, edge-directed interpolation has been introduced in different forms. One variant, new edge-directed interpolation (NEDI), has successfully exploited the 'geometric duality' that links the low-resolution image to its corresponding high-resolution image. It has been demonstrated that for scalar images, NEDI is able to produce better results than non-adaptive traditional methods, both visually and quantitatively. In this work, we return to the root of NEDI as a least-squares estimation method of neighborhood patterns and propose a robust scheme to improve it. The improvement is twofold: firstly, a robust least-squares technique is used to improve NEDI's performance to outliers and noise; secondly, the NEDI algorithm is extended with the recently proposed non-local mean estimation scheme. Moreover, the edge-directed concept is applied to the interpolation of multi-valued diffusion-weighted images. The framework is tested on phantom scalar images and real diffusion images, and is shown to achieve better results than the non-adaptive methods as well as NEDI, in terms of visual quality as well as quantitative measures.