Image up-sampling using total-variation regularization with a new observation model

This paper presents a new formulation of the regularized image up-sampling problem that incorporates models of the image acquisition and display processes. We give a new analytic perspective that justifies the use of total-variation regularization from a signal processing perspective, based on an analysis that specifies the requirements of edge-directed filtering. This approach leads to a new data fidelity term that has been coupled with a total-variation regularizer to yield our objective function. This objective function is minimized using a level-sets motion that is based on the level-set method, with two types of motion that interact simultaneously. A new choice of these motions leads to a stable solution scheme that has a unique minimum. One aspect of the human visual system, perceptual uniformity, is treated in accordance with the linear nature of the data fidelity term. The method was implemented and has been verified to provide improved results, yielding crisp edges without introducing ringing or other artifacts.