Robust edge-directed interpolation of magnetic resonance images

Image interpolation is intrinsically a severely under-determined inverse problem. Traditional non-adaptive methods utilize certain models that fail to respect local image statistics around edges of image structures. In practice, this results in artifacts such as jagged edges and/or blurring. To overcome this short-coming, the concept of edge-directed interpolation has been introduced in different forms. One interesting variant, New Edge Directed Interpolation (NEDI) [9], has successfully exploited the “geometric duality” that linked between the low-resolution (LR) image and its corresponding high-resolution (HR) 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 comes two-folds: firstly, a robust least-squares technique is used to improve NEDI's performance to noise; secondly, the NEDI algorithm is extended with the recently proposed Non-Local Mean (NLM) estimation scheme. Moreover, the edge-directed concept is applied to the interpolation of multivalued diffusion weighted images (DWI). The framework is tested on phantom scalar images and real diffusion images, and is shown to be able to achieve better results than the non-adaptive methods, in terms of visual quality as well as quantitative measures.