# Characterizations of Differentiability, Smoothing Techniques and DC Programming with Applications to Image Reconstructions

In this paper, we study characterizations of differentiability for real-valued functions based on generalized differentiation. These characterizations provide the mathematical foundation for Nesterov's smoothing techniques in infinite dimensions. As an application, we provide a simple approach to image reconstructions based on Nesterov's smoothing techniques and DC programming that involves the $\ell_1-\ell_2$ regularization.