Image Reconstruction From Random Samples With Multiscale Hybrid Parametric and Nonparametric Modeling

Statistical image modeling is of central importance to many image-processing tasks that are ill-posed in nature. Existing image models can be categorized as parametric models and nonparametric models according to the statistical techniques used. In this paper, we develop a hybrid image reconstruction (HIR) algorithm from sparse random samples using parametric and nonparametric modeling of images. More specifically, the modeling strength of the parametric and nonparametric techniques are combined within a multiscale framework. The linear autoregressive parametric model and kernel regressive nonparametric models are used to explore the interscale and intrascale dependencies of the image, respectively. The proposed HIR algorithm is capable of recovering the image from very sparse samples (e.g., 5%), and experimental results suggest that the proposed algorithm achieves noticeable improvement over some of the existing approaches in terms of both peak signal-to-noise ratio and subjective qualities of the reconstruction results.