Enhancement of contrast and sharpness of an image is required in many applications. Unsharp masking is a classical tool for sharpness enhancement. We propose a generalized unsharp masking algorithm using the exploratory data model as a unified framework. The proposed algorithm is designed to address three issues: (1) simultaneously enhancing contrast and sharpness by means of individual treatment of the model component and the residual, (2) reducing the halo effect by means of an edge-preserving filter, and (3) solving the out-of-range problem by means of log-ratio and tangent operations. We also present a study of the properties of the log-ratio operations and reveal a new connection between the Bregman divergence and the generalized linear systems. This connection not only provides a novel insight into the geometrical property of such systems, but also opens a new pathway for system development. We present a new system called the tangent system which is based upon a specific Bregman divergence. Experimental results, which are comparable to recently published results, show that the proposed algorithm is able to significantly improve the contrast and sharpness of an image. In the proposed algorithm, the user can adjust the two parameters controlling the contrast and sharpness to produce the desired results. This makes the proposed algorithm practically useful.