Informatica

Medical X-ray images are prevalent and are the least expensive diagnostic imaging method available widely. The handling of film processing and digitization introduces noise in X-ray images and suppressing such noise is an important step in medical image analysis. In this work, we use an adaptive total variation regularization method for removing quantum noise from X-ray images. By utilizing an edge indicator measure along with the well-known edge preserving total variation regularization, we obtain noise removal without losing salient features. Experimental results on different X-ray images indicate the promise of our approach. Synthetic examples are given to compare the performance of our scheme with traditional total variation and anisotropic diffusion methods from the literature. Overall, our proposed approach obtains better results in terms of visual appearance as well as with respect to different error metrics and structural similarity.

The paper studies stochastic optimization problems in Reproducing Kernel Hilbert Spaces (RKHS). The objective function of such problems is a mathematical expectation functional depending on decision rules (or strategies), i.e. on functions of observed random parameters. Feasible rules are restricted to belong to a RKHS. This kind of problems arises in on-line decision making and in statistical learning theory. We solve the problem by sample average approximation combined with Tihonov's regularization and establish sufficient conditions for uniform convergence of approximate solutions with probability one, jointly with a rule for downward adjustment of the regularization factor with increasing sample size.