SURE-Based Non-Local Means

Non-local means (NLM) provides a powerful framework for denoising. However, there are a few parameters of the algorithm-most notably, the width of the smoothing kernel-that are data-dependent and difficult to tune. Here, we propose to use Stein's unbiased risk estimate (SURE) to monitor the mean square error (MSE) of the NLM algorithm for restoration of an image corrupted by additive white Gaussian noise. The SURE principle allows to assess the MSE without knowledge of the noise-free signal. We derive an explicit analytical expression for SURE in the setting of NLM that can be incorporated in the implementation at low computational cost. Finally, we present experimental results that confirm the optimality of the proposed parameter selection

Nonparametric Estimation for SDE with Sparsely Sampled Paths: an FDA Perspective

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed sparsely and irregularly on the unit interval, and subject to additive noise corruption. By \textit{sparse} we intend to mean that the number of measurements per path can be arbitrary (as small as two), and remain constant with respect to $n$. We focus on time-inhomogeneous SDE of the form $dX_t = \mu(t)X_t^{\alpha}dt + \sigma(t)X_t^{\beta}dW_t$, where $\alpha \in \{0,1\}$ and $\beta \in \{0,1/2,1\}$, which includes prominent examples such as Brownian motion, Ornstein-Uhlenbeck process, geometric Brownian motion, and Brownian bridge. Our estimators are constructed by relating the local (drift/diffusion) parameters of the diffusion to their global parameters (mean/covariance, and their derivatives) by means of an apparently novel PDE. This allows us to use methods inspired by functional data analysis, and pool information across the sparsely measured paths. The methodology we develop is fully non-parametric and avoids any functional form specification on the time-dependency of either the drift function or the diffusion function. We establish almost sure uniform asymptotic convergence rates of the proposed estimators as the number of observed curves $n$ grows to infinity. Our rates are non-asymptotic in the number of measurements per path, explicitly reflecting how different sampling frequency might affect the speed of convergence. Our framework suggests possible further fruitful interactions between FDA and SDE methods in problems with replication

Renal Association Clinical Practice Guideline on Haemodialysis

© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.This guideline is written primarily for doctors and nurses working in dialysis units and related areas of medicine in the UK, and is an update of a previous version written in 2009. It aims to provide guidance on how to look after patients and how to run dialysis units, and provides standards which units should in general aim to achieve. We would not advise patients to interpret the guideline as a rulebook, but perhaps to answer the question: "what does good quality haemodialysis look like?"The guideline is split into sections: each begins with a few statements which are graded by strength (1 is a firm recommendation, 2 is more like a sensible suggestion), and the type of research available to back up the statement, ranging from A (good quality trials so we are pretty sure this is right) to D (more like the opinion of experts than known for sure). After the statements there is a short summary explaining why we think this, often including a discussion of some of the most helpful research. There is then a list of the most important medical articles so that you can read further if you want to - most of this is freely available online, at least in summary form.A few notes on the individual sections: 1. This section is about how much dialysis a patient should have. The effectiveness of dialysis varies between patients because of differences in body size and age etc., so different people need different amounts, and this section gives guidance on what defines "enough" dialysis and how to make sure each person is getting that. Quite a bit of this section is very technical, for example, the term "eKt/V" is often used: this is a calculation based on blood tests before and after dialysis, which measures the effectiveness of a single dialysis session in a particular patient. 2. This section deals with "non-standard" dialysis, which basically means anything other than 3 times per week. For example, a few people need 4 or more sessions per week to keep healthy, and some people are fine with only 2 sessions per week - this is usually people who are older, or those who have only just started dialysis. Special considerations for children and pregnant patients are also covered here. 3. This section deals with membranes (the type of "filter" used in the dialysis machine) and "HDF" (haemodiafiltration) which is a more complex kind of dialysis which some doctors think is better. Studies are still being done, but at the moment we think it's as good as but not better than regular dialysis. 4. This section deals with fluid removal during dialysis sessions: how to remove enough fluid without causing cramps and low blood pressure. Amongst other recommendations we advise close collaboration with patients over this. 5. This section deals with dialysate, which is the fluid used to "pull" toxins out of the blood (it is sometimes called the "bath"). The level of things like potassium in the dialysate is important, otherwise too much or too little may be removed. There is a section on dialysate buffer (bicarbonate) and also a section on phosphate, which occasionally needs to be added into the dialysate. 6. This section is about anticoagulation (blood thinning) which is needed to stop the circuit from clotting, but sometimes causes side effects. 7. This section is about certain safety aspects of dialysis, not seeking to replace well-established local protocols, but focussing on just a few where we thought some national-level guidance would be useful. 8. This section draws together a few aspects of dialysis which don't easily fit elsewhere, and which impact on how dialysis feels to patients, rather than the medical outcome, though of course these are linked. This is where home haemodialysis and exercise are covered. There is an appendix at the end which covers a few aspects in more detail, especially the mathematical ideas. Several aspects of dialysis are not included in this guideline since they are covered elsewhere, often because they are aspects which affect non-dialysis patients too. This includes: anaemia, calcium and bone health, high blood pressure, nutrition, infection control, vascular access, transplant planning, and when dialysis should be started.Peer reviewe

National evaluation of Sure Start local programmes: an economic perspective

The first 524 Sure Start local programmes (SSLPs) were established between 1999 and 2003. They were aimed at families with children up to the age of 4 living in disadvantaged areas. The aim was to bring together early education, childcare, health services and family support to promote the physical, intellectual and social development of babies and children. This report discusses the economic issues arising out of the evaluation of the impact of Sure Start local programmes in England. It takes the outcomes for children and families at the age of five years reported in the National Evaluation of Sure Start and where possible estimates economic values for those outcomes. Where a direct estimation of economic value is not possible at this stage, probable sources of future economic values are discussed. It should be read in conjunction with the impact report, which describes the details of the methodology of the study and the full range of outcomes for children and their families when the children were 5-years-old

The impact of Sure Start local programmes on seven year olds and their families

This research report presents the findings of a longitudinal study into the impact of Sure Start local programmes (SSLPs) on 7-year-olds and their families. In assessing the impact of SSLPs on child and family functioning over time, the evaluation followed up over 5,000 7-year-olds and their families in 150 SSLP areas who were initially studied when the children were 9 months and 3- and 5-years-old

The impact of Sure Start Local Programmes on five year olds and their families

The ultimate goal of Sure Start Local Programmes (SSLPs) was to enhance the life chances for young children growing up in disadvantaged neighbourhoods. Children in these communities are at risk of doing poorly at school, having trouble with peers and agents of authority (i.e., parents, teachers), and ultimately experiencing compromised life chances. In this report children and families who were seen at 9 months and 3 years of age in the NESS or MCS longitudinal studies are compared to determine whether differences in child and family functioning found at 3 years of age persist until 5 years of age, and whether any other differences emerge

The impact of Sure Start local programmes on three-year-olds and their families

This evaluation found that living in a Sure Start Local Programme (SSLP) area was associated with positive impacts on 5 of the 14 outcomes investigated. The analysis of the most recent data shows beneficial effects for almost all children and families living in SSLP areas and provides almost no evidence of adverse effects on population sub-groups such as workless or lone-parent families. These results are in marked contrast to the findings of the initial study published in 2005. Although methodological variations may account for differences in findings across the two phases of the evaluation, the researchers argue that it is eminently possible that the differing results accurately reflect the contrasting experiences of SSLP children and families in the two phases. They argue that the three-year-olds in the latest study have benefited from exposure to more mature and developed local programmes throughout their young lives