Random action of compact Lie groups and minimax estimation of a mean pattern

This paper considers the problem of estimating a mean pattern in the setting of Grenander's pattern theory. Shape variability in a data set of curves or images is modeled by the random action of elements in a compact Lie group on an infinite dimensional space. In the case of observations contaminated by an additive Gaussian white noise, it is shown that estimating a reference template in the setting of Grenander's pattern theory falls into the category of deconvolution problems over Lie groups. To obtain this result, we build an estimator of a mean pattern by using Fourier deconvolution and harmonic analysis on compact Lie groups. In an asymptotic setting where the number of observed curves or images tends to infinity, we derive upper and lower bounds for the minimax quadratic risk over Sobolev balls. This rate depends on the smoothness of the density of the random Lie group elements representing shape variability in the data, which makes a connection between estimating a mean pattern and standard deconvolution problems in nonparametric statistics

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Effects of diet versus gastric bypass on metabolic function in diabetes

BackgroundSome studies have suggested that in people with type 2 diabetes, Roux-en-Y gastric bypass has therapeutic effects on metabolic function that are independent of weight loss.MethodsWe evaluated metabolic regulators of glucose homeostasis before and after matched (approximately 18%) weight loss induced by gastric bypass (surgery group) or diet alone (diet group) in 22 patients with obesity and diabetes. The primary outcome was the change in hepatic insulin sensitivity, assessed by infusion of insulin at low rates (stages 1 and 2 of a 3-stage hyperinsulinemic euglycemic pancreatic clamp). Secondary outcomes were changes in muscle insulin sensitivity, beta-cell function, and 24-hour plasma glucose and insulin profiles.ResultsWeight loss was associated with increases in mean suppression of glucose production from baseline, by 7.04 μmol per kilogram of fat-free mass per minute (95% confidence interval [CI], 4.74 to 9.33) in the diet group and by 7.02 μmol per kilogram of fat-free mass per minute (95% CI, 3.21 to 10.84) in the surgery group during clamp stage 1, and by 5.39 (95% CI, 2.44 to 8.34) and 5.37 (95% CI, 2.41 to 8.33) μmol per kilogram of fat-free mass per minute in the two groups, respectively, during clamp stage 2; there were no significant differences between the groups. Weight loss was associated with increased insulin-stimulated glucose disposal, from 30.5±15.9 to 61.6±13.0 μmol per kilogram of fat-free mass per minute in the diet group and from 29.4±12.6 to 54.5±10.4 μmol per kilogram of fat-free mass per minute in the surgery group; there was no significant difference between the groups. Weight loss increased beta-cell function (insulin secretion relative to insulin sensitivity) by 1.83 units (95% CI, 1.22 to 2.44) in the diet group and by 1.11 units (95% CI, 0.08 to 2.15) in the surgery group, with no significant difference between the groups, and it decreased the areas under the curve for 24-hour plasma glucose and insulin levels in both groups, with no significant difference between the groups. No major complications occurred in either group.ConclusionsIn this study involving patients with obesity and type 2 diabetes, the metabolic benefits of gastric bypass surgery and diet were similar and were apparently related to weight loss itself, with no evident clinically important effects independent of weight loss. (Funded by the National Institutes of Health and others; ClinicalTrials.gov number, NCT02207777.)

Continuous glucose monitoring sensors: Past, present and future algorithmic challenges

Continuous glucose monitoring (CGM) sensors are portable devices that allow measuring and visualizing the glucose concentration in real time almost continuously for several days and are provided with hypo/hyperglycemic alerts and glucose trend information. CGM sensors have revolutionized Type 1 diabetes (T1D) management, improving glucose control when used adjunctively to self-monitoring blood glucose systems. Furthermore, CGM devices have stimulated the development of applications that were impossible to create without a continuous-time glucose signal, e.g., real-time predictive alerts of hypo/hyperglycemic episodes based on the prediction of future glucose concentration, automatic basal insulin attenuation methods for hypoglycemia prevention, and the artificial pancreas. However, CGM sensors’ lack of accuracy and reliability limited their usability in the clinical practice, calling upon the academic community for the development of suitable signal processing methods to improve CGM performance. The aim of this paper is to review the past and present algorithmic challenges of CGM sensors, to show how they have been tackled by our research group, and to identify the possible future ones

Fast rate of convergence in high dimensional linear discriminant analysis

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when dimension p is larger than sample size n. The corresponding theoretical results are non asymptotic lower bounds. On the other hand, we propose two discrimination procedures based on dimensionality reduction and provide associated rates of convergence which can be O(log(p)/n) under sparsity assumptions. Finally all our results rely on a theorem that provides simple sharp relations between the excess risk and an estimation error associated to the geometric parameters defining the used discrimination rule