Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Study of diffusion weighted MRI as a predictive biomarker of response during radiotherapy for high and intermediate risk squamous cell cancer of the oropharynx: The MeRInO study

Introduction and background: A significant proportion of patients with intermediate and high risk squamous cell cancer of the oropharynx (OPSCC) continue to relapse locally despite radical chemoradiotherapy (CRT). The toxicity of the current combination of intensified dose per fraction radiotherapy and platinum based chemotherapy limits further uniform intensification. If a predictive biomarker for outcomes from CRT can be identified during treatment then individualised and adaptive treatment strategies may be employed. Methods/design: The MeRInO study is a prospective observational imaging study of patients with intermediate and high risk, locally advanced OPSCC receiving radical RT or concurrent CRT Patients undergo diffusion weighted MRI prior to treatment (MRI_1) and during the third week of RT (MRI_2). Apparent diffusion coefficient (ADC) measurements will be made on each scan for previously specified target lesions (primary and lymph nodes) and change in ADC calculated. Patients will be followed up and disease status for each target lesion noted. The primary aim of the MeRInO study is to determine the threshold change in ADC from baseline to week 3 of RT that may identify the sub-group of non-responders during treatment. Discussion: The use of DW-MRI as a predictive biomarker during RT for SCC H&N is in its infancy but studies to date have found that response to treatment may indeed be predicted by comparison of DW-MRI carried out before and during treatment. However, previous studies have included all sub-sites and biological sub-types. Establishing ADC thresholds that predict for local failure is an essential step towards using DW-MRI to improve the therapeutic ratio in treating SCC H&N. This would be done most robustly in a specific H&N sub-site and in sub-types with similar biological behaviour. The MeRInO study will help establish these thresholds in OPSCC

Estimating local car ownership models

Many studies in the transport demand literature have shown that income is an important factor in determining how many cars a household owns. When the models used to measure the strength of this relationship are estimated on cross-sectional data, they typically yield one overall value as the estimate. Local circumstances will, however, vary. This paper illustrates the use of the Geographically Weighted Regression technique to estimate the individual strength of this relationship for each of the United Kingdom electoral wards. Use of this type of model enables a wards’ income elasticity to be based on both the local estimate of the strength of this relationship and the current local level of car ownership. How the use of this local elasticity changes future forecasts of the size of the vehicle fleet is illustrated

Tensor Regression with Applications in Neuroimaging Data Analysis

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data.Comment: 27 pages, 4 figure