Reconciling Bayesian and Total Variation Methods for Binary Inversion

A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization. On the other hand, sparse or noisy data often demands a probabilistic approach to the reconstruction of images, to enable uncertainty quantification; the Bayesian approach to inversion is a natural framework in which to carry this out. The link between Bayesian inversion methods and perimeter regularization, however, is not fully understood. In this paper two links are studied: (i) the MAP objective function of a suitably chosen phase-field Bayesian approach is shown to be closely related to a least squares plus perimeter regularization objective; (ii) sample paths of a suitably chosen Bayesian level set formulation are shown to possess finite perimeter and to have the ability to learn about the true perimeter. Furthermore, the level set approach is shown to lead to faster algorithms for uncertainty quantification than the phase field approach

Reconciling Bayesian and Perimeter Regularization for Binary Inversion

A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of total variation. On the other hand, sparse or noisy data often demand a probabilistic approach to the reconstruction of images, to enable uncertainty quantification; the Bayesian approach to inversion, which itself introduces a form of regularization, is a natural framework in which to carry this out. In this paper the link between Bayesian inversion methods and perimeter regularization is explored. In this paper two links are studied: (i) the maximum a posteriori objective function of a suitably chosen Bayesian phase-field approach is shown to be closely related to a least squares plus perimeter regularization objective; (ii) sample paths of a suitably chosen Bayesian level set formulation are shown to possess a finite perimeter and to have the ability to learn about the true perimeter

The decay Bs -> mu+ mu-: updated SUSY constraints and prospects

We perform a study of the impact of the recently released limits on BR(Bs -> mu+ mu-) by LHCb and CMS on several SUSY models. We show that the obtained constraints can be superior to those which are derived from direct searches for SUSY particles in some scenarios, and the use of a double ratio of purely leptonic decays involving Bs -> mu+ mu- can further strengthen such constraints. We also discuss the experimental sensitivity and prospects for observation of Bs -> mu+ mu- during the sqrt(s)=7 TeV run of the LHC, and its potential implications.Comment: 30 pages, 21 figures. v2: Improved discussion of constraints from B -> tau nu, references adde

Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface

In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable conditions on the spatial grid size, the time step and the interface width we obtain stability and error bounds with respect to natural norms. Furthermore, we present test calculations that confirm our analysis