Total variation regularization for manifold-valued data

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoising images which take their values in a manifold. We apply our algorithms to diffusion tensor images, interferometric SAR images as well as sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging) we show the convergence of the proposed TV minimizing algorithms to a global minimizer

Jump-sparse and sparse recovery using Potts functionals

We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and provide relations to sparsity problems. We then propose a new optimization method for these functionals which is based on dynamic programming and the alternating direction method of multipliers (ADMM). A series of experiments shows that the proposed method yields very satisfactory jump-sparse and sparse reconstructions, respectively. We highlight the capability of the method by comparing it with classical and recent approaches such as TV minimization (jump-sparse signals), orthogonal matching pursuit, iterative hard thresholding, and iteratively reweighted $\ell^1$ minimization (sparse signals)

Irregular Sampling of the Radon Transform of Bandlimited Functions

Publication in the conference proceedings of SampTA, Bremen, Germany, 201

Mumford-Shah and Potts Regularization for Manifold-Valued Data with Applications to DTI and Q-Ball Imaging

Mumford-Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and non-convex, they are computationally challenging even for scalar data. For manifold-valued data, the problem becomes even more involved since typical features of vector spaces are not available. In this paper, we propose algorithms for Mumford-Shah and for Potts regularization of manifold-valued signals and images. For the univariate problems, we derive solvers based on dynamic programming combined with (convex) optimization techniques for manifold-valued data. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging), we show that our algorithms compute global minimizers for any starting point. For the multivariate Mumford-Shah and Potts problems (for image regularization) we propose a splitting into suitable subproblems which we can solve exactly using the techniques developed for the corresponding univariate problems. Our method does not require any a priori restrictions on the edge set and we do not have to discretize the data space. We apply our method to diffusion tensor imaging (DTI) as well as Q-ball imaging. Using the DTI model, we obtain a segmentation of the corpus callosum

The L1-Potts functional for robust jump-sparse reconstruction

We investigate the non-smooth and non-convex $L^1$-Potts functional in discrete and continuous time. We show $\Gamma$-convergence of discrete $L^1$-Potts functionals towards their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer. For the discrete $L^1$-Potts problem, we introduce an $O(n^2)$ time and $O(n)$ space algorithm to compute an exact minimizer. We apply $L^1$-Potts minimization to the problem of recovering piecewise constant signals from noisy measurements $f.$ It turns out that the $L^1$-Potts functional has a quite interesting blind deconvolution property. In fact, we show that mildly blurred jump-sparse signals are reconstructed by minimizing the $L^1$-Potts functional. Furthermore, for strongly blurred signals and known blurring operator, we derive an iterative reconstruction algorithm

Prevention of ventilator‑associated pneumonia by noble metal coating of endotracheal tubes: a multi‑center, randomized, double‑blind study

BACKGROUND: Ventilator-associated pneumonia (VAP) causes increased mortality, prolonged hospital stay and increased healthcare costs. Prevention of VAP in intensive care units (ICUs) is currently based on several measures, and application of noble metal coating on medical devices has been shown to inhibit the bacterial adherence of microorganisms to the surface. The objective of this study was to evaluate the potential benefit of noble metal coating of endotracheal tubes for the prevention of VAP. METHODS: This was a multi-center, randomized, controlled, double-blind, prospective study including ventilated patients from nine ICUs from four hospital sites in Belgium. Patients were randomly intubated with identical appearing noble metal alloy (NMA) coated (NMA-coated group) or non-coated (control group) endotracheal tubes (ETT). Primary endpoint was the incidence of VAP. Secondary endpoints were the proportion of antibiotic days during ICU stay and tracheal colonization by pathogenic bacteria. RESULTS: In total, 323 patients were enrolled, 168 in the NMA-coated group and 155 in the control group. During ventilation, VAP occurred in 11 patients (6.5%) in the NMA-coated group and in 18 patients (11.6%) in the control group (p  = 0.11). A higher delay in VAP occurrence was observed in the NMA-coated group compared with the control group by Cox proportional hazards regression analysis (HR 0.41, 95% CI 0.19–0.88, p  = 0.02). The number of antibiotic days was 58.8% of the 1,928 ICU days in the NMA-coated group and 65.4% of the 1774 ICU days in the control group (p  = 0.06). Regarding tracheal colonization, bacteria occurred in 38 of 126 patients in the NMA-coated group (30.2%) and in 37 of 109 patients in the control group (33.9%) (p  = 0.57). CONCLUSIONS: This study provides preliminary evidence to support the benefit of noble metal coating in the prevention of VAP. A confirmatory study in a larger population would be valuable. Trial registration: Clinical trial number: NCT04242706 (http://www.clinicaltrials.gov

Minimal information for studies of extracellular vesicles 2018 (MISEV2018):a position statement of the International Society for Extracellular Vesicles and update of the MISEV2014 guidelines

The last decade has seen a sharp increase in the number of scientific publications describing physiological and pathological functions of extracellular vesicles (EVs), a collective term covering various subtypes of cell-released, membranous structures, called exosomes, microvesicles, microparticles, ectosomes, oncosomes, apoptotic bodies, and many other names. However, specific issues arise when working with these entities, whose size and amount often make them difficult to obtain as relatively pure preparations, and to characterize properly. The International Society for Extracellular Vesicles (ISEV) proposed Minimal Information for Studies of Extracellular Vesicles (“MISEV”) guidelines for the field in 2014. We now update these “MISEV2014” guidelines based on evolution of the collective knowledge in the last four years. An important point to consider is that ascribing a specific function to EVs in general, or to subtypes of EVs, requires reporting of specific information beyond mere description of function in a crude, potentially contaminated, and heterogeneous preparation. For example, claims that exosomes are endowed with exquisite and specific activities remain difficult to support experimentally, given our still limited knowledge of their specific molecular machineries of biogenesis and release, as compared with other biophysically similar EVs. The MISEV2018 guidelines include tables and outlines of suggested protocols and steps to follow to document specific EV-associated functional activities. Finally, a checklist is provided with summaries of key points