Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics of projections of the residuals on a given set of sub-spaces in the image-space of the operator. We prove general consistency and convergence rate results in the framework of Bregman-divergences which allows for a vast range of penalty functionals. Various examples that indicate the applicability of our approach will be discussed. We will illustrate in the context of signal and image processing that the presented method constitutes a locally adaptive reconstruction method

Multiscale Change-Point Inference

We introduce a new estimator SMUCE (simultaneous multiscale change-point estimator) for the change-point problem in exponential family regression. An unknown step function is estimated by minimizing the number of change-points over the acceptance region of a multiscale test at a level \alpha. The probability of overestimating the true number of change-points K is controlled by the asymptotic null distribution of the multiscale test statistic. Further, we derive exponential bounds for the probability of underestimating K. By balancing these quantities, \alpha will be chosen such that the probability of correctly estimating K is maximized. All results are even non-asymptotic for the normal case. Based on the aforementioned bounds, we construct asymptotically honest confidence sets for the unknown step function and its change-points. At the same time, we obtain exponential bounds for estimating the change-point locations which for example yield the minimax rate O(1/n) up to a log term. Finally, SMUCE asymptotically achieves the optimal detection rate of vanishing signals. We illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions. The performance of the proposed multiscale approach is illustrated by simulations and in two cutting-edge applications from genetic engineering and photoemission spectroscopy

Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics

In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in [Frick K, Marnitz P, and Munk A. "Statistical multiresolution Dantzig estimation in imaging: Fundamental concepts and algorithmic framework". Electron. J. Stat., 6:231-268, 2012]. It constitutes a variational regularization technique that uses an supremum-type distance measure as data-fidelity combined with a convex cost functional. The resulting convex optimization problem is approached by a combination of an inexact alternating direction method of multipliers and Dykstra's projection algorithm. We describe a novel method for balancing data-fit and regularity that is fully automatic and allows for a sound statistical interpretation. The performance of our estimation approach is studied for various problems in imaging. Among others, this includes deconvolution problems that arise in Poisson nanoscale fluorescence microscopy

10 years of experience with autogenous microsurgical lymphvessel-transplantation

The authors report their experience with the autogenous microsurgical lymphvessel transplantation for the treatment of upper (n = 60, 55 females and 5 males) and lower (n = 35, 10 females and 25 males, primary lyphredemas = 11, secondary lymphredemas = 24) limb edemas. Regarding the volume measurements before and after lymphvessel - transplantation in 58 patients there was a reduction of volume differences between healthy and affected arms of more than the half in 76 % of the patients after a mean follow-up period of 2 1/2 years. In 28 patients with unilateral redemas of the lower extremities the volume reduction after a mean follow-up period of I 1/2 year compared to the healthy legs was more than 50 % in 20 patients. As complications in the early period 2 postoperative erysipelas were seen. One patient developed a Iymph cyst in the groin and one patient had a postthrombotic lower leg rederna. The authors conclude that lymphvessel transplantations therefore seem to be a method to enhance significantly the lymphatic transport if by conservation me ans alone no long term success is seen

How To Predict A Pop-Up Store – Developing A Data Based Framework For Digitizing The Location Choice Process And Prototyping At The Case Of St. Gallen (Ch)

We target identifying the needs for the fulfillment of location factors of pop-up retailers being determined by their core motivations and retail sector affiliation. We undertake to do both, to qualify, and to quantify their needs to gain at end of the day a profound description of various pop-up retail patterns. Through the use of a mixed-methods approach containing qualitative research through conducting interviews and qualitative content analysis as well as quantitative fulfillment of location factors through data analysis of multiple location data sources like Open Street Map, we try to gain first indications towards a deeper understanding of pop-up location decisions as well as to validate our hypothesis of the existence of pop-up retail patterns. We were able to validate three retail patterns through our qualitative research. Furthermore, we saw differences reflecting the particular motivations of running the ephemeral retail project. Despite our small shown sample of quantitative data for St. Gallen, we figured out the first indications that store density is a suitable indicator to understand pop-up retailers’ locations’ decisions. Nevertheless, there is a need to continue research in both terms, more quantitative data like footfall and financial transactions (turnovers) as well as bigger, more representative samples. Within the undertaken literature review we saw a lack of research in gaining a deeper understanding of the nature of pop-up retail in terms of location needs and how location decisions are made. We present results that may deal as a foundation for upcoming research. Moreover, we contribute to the state of research in patterns of retail location choice through a data-driven approach, which presents reasonable insights into the field of location intelligence of temporary retail