Image interpolation based on non-local geometric similarities

Image interpolation refers to constructing a high-resolution (HR) image from a low-resolution (LR) image. Traditionally, an HR image can be produced from an observed LR image via the polynomial-based interpolation (bi-linear or bi-cubic interpolations, involving a small number of neighbors around each interpolated position). The advanced interpolation makes use of the so-called 'geometric similarity' to design a set of optimal interpolation weighting coefficients. However, better geometric similarities can perhaps be found from a non-local area within the LR source image or even from other but similar images (possibly with higher resolutions). Based on this fact, we propose in this paper a non-local geometric similarity based interpolation scheme to construct HR images. In our proposed method, optimal weighting coefficients are determined by solving a regularized least squares problem which is built upon a number of dual reference patches drawn from the observed LR image and regularized by the variation of directional gradients of the image patch. Experimental results demonstrate that our proposed method offers a remarkable quality improvement, both objectively and subjectively.