An Adaptable $k$ -Nearest Neighbors Algorithm for MMSE Image Interpolation

We propose an image interpolation algorithm that is nonparametric and learning-based, primarily using an adaptive
k
-nearest neighbor algorithm with global considerations through Markov random fields. The empirical nature of the proposed algorithm ensures image results that are data-driven and, hence, reflect ldquoreal-worldrdquo images well, given enough training data. The proposed algorithm operates on a local window using a dynamic
k
-nearest neighbor algorithm, where
k
differs from pixel to pixel: small for test points with highly relevant neighbors and large otherwise. Based on the neighbors that the adaptable
k
provides and their corresponding relevance measures, a weighted minimum mean squared error solution determines implicitly defined filters specific to low-resolution image content without yielding to the limitations of insufficient training. Additionally, global optimization via single pass Markov approximations, similar to cited nearest neighbor algorithms, provides additional weighting for filter generation. The approach is justified in using a sufficient quantity of training per test point and takes advantage of image properties. For in-depth analysis, we compare to existing methods and draw parallels between intuitive concepts including classification and ideas introduced by other nearest neighbor algorithms by explaining manifolds in low and high dimensions.