Linear interpolation of biomedical images using a data-adaptive kernel

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters from the data, we introduce two possible error criteria; namely, Gaussian maximum-likelihood, and least-squares autocorrelation fit. Exploiting the link between autoregressive models and spline approximation, we use our approach to adapt interpolation parameters to a given image. Our numerical results demonstrate that our adaptive approach yields higher SNR values compared to classical polynomial splines for the task of image scaling. They also indicate that our least-squares-based error criterion nearly achieves the oracle performance for parameter estimation, which provides further support to the practical relevance of our model.