A total variation discontinuous Galerkin approach for image restoration

The focal point of this paper is to propose and analyze a P 0 discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.

Digital vs. conventional implant prosthetic workflows: a cost/time analysis.

OBJECTIVES The aim of this prospective cohort trial was to perform a cost/time analysis for implant-supported single-unit reconstructions in the digital workflow compared to the conventional pathway. MATERIALS AND METHODS A total of 20 patients were included for rehabilitation with 2 × 20 implant crowns in a crossover study design and treated consecutively each with customized titanium abutments plus CAD/CAM-zirconia-suprastructures (test: digital) and with standardized titanium abutments plus PFM-crowns (control conventional). Starting with prosthetic treatment, analysis was estimated for clinical and laboratory work steps including measure of costs in Swiss Francs (CHF), productivity rates and cost minimization for first-line therapy. Statistical calculations were performed with Wilcoxon signed-rank test. RESULTS Both protocols worked successfully for all test and control reconstructions. Direct treatment costs were significantly lower for the digital workflow 1815.35 CHF compared to the conventional pathway 2119.65 CHF [P = 0.0004]. For subprocess evaluation, total laboratory costs were calculated as 941.95 CHF for the test group and 1245.65 CHF for the control group, respectively [P = 0.003]. The clinical dental productivity rate amounted to 29.64 CHF/min (digital) and 24.37 CHF/min (conventional) [P = 0.002]. Overall, cost minimization analysis exhibited an 18% cost reduction within the digital process. CONCLUSION The digital workflow was more efficient than the established conventional pathway for implant-supported crowns in this investigation.

A Logarithmic Image Prior for Blind Deconvolution

Blind Deconvolution consists in the estimation of a sharp image and a blur kernel from an observed blurry image. Because the blur model admits several solutions it is necessary to devise an image prior that favors the true blur kernel and sharp image. Many successful image priors enforce the sparsity of the sharp image gradients. Ideally the L0 “norm” is the best choice for promoting sparsity, but because it is computationally intractable, some methods have used a logarithmic approximation. In this work we also study a logarithmic image prior. We show empirically how well the prior suits the blind deconvolution problem. Our analysis confirms experimentally the hypothesis that a prior should not necessarily model natural image statistics to correctly estimate the blur kernel. Furthermore, we show that a simple Maximum a Posteriori formulation is enough to achieve state of the art results. To minimize such formulation we devise two iterative minimization algorithms that cope with the non-convexity of the logarithmic prior: one obtained via the primal-dual approach and one via majorization-minimization.