This document discusses image reconstruction techniques using high-order Markov random field (HMRF) models and half-quadratic minimization relaxation (HWMRF). It presents equations for HMRF that incorporate higher-order cliques to model image properties. Reconstruction is achieved by alternately updating the high-resolution image and hyperparameters to minimize an objective function combining data and regularization terms. Examples show reconstructed surveillance images using HMRF and HWMRF, with the latter producing sharper details while preserving edges.