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扩散 MRI 模型中的低信噪比问题AI 解读

Noise is a common issue for all magnetic resonance imaging (MRI) techniques such as diffusion MRI and obviously leads to variability of the estimates in any model describing the data. Increasing spatial resolution in MR experiments further diminishes the signal-to-noise ratio (SNR). However, with low SNR the expected signal deviates from the true value. Common modeling approaches therefore lead to a bias in estimated model parameters. Adjustments require an analysis of the…

图像去噪：逐点自适应方法AI 解读

A new method of pointwise adaptation has been proposed and studied in Spokoiny [(1998) Ann. Statist.26 1356-1378] in the context of estimation of piecewise smooth univariate functions. The present paper extends that method to estimation of bivariate grey-scale images composed of large homogeneous regions with smooth edges and observed with noise on a gridded design. The proposed estimator $\hat{f}(x)$ at a point x is simply the average of observations over a window $\widehat{U}(x)$…

结构自适应降维方法AI 解读

We propose a new method of effective dimension reduction for a multi-index model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension $m$ of the index space does not exceed 3, this space can be estimated with the rate $n^{-1/2}$ under rather mild…

多类型 Boolean 模型中团块边界的维数AI 解读

In a fascinating article on models for particulate microstructure, Hermann and Ohser argue that the superposition of stochastically independent Boolean models may be thought of as producing sets whose boundaries have unusual properties of dimension. Hermann and Ohser employ such superposition models to analyse the particulate structure of rust. In the present paper we provide a theoretical foundation for their work, with respect to both the definition of dimension and its…

短程与长程相关误差下非参数回归的带宽选择AI 解读

We analyse methods based on the block bootstrap and leave-out cross-validation, for choosing the bandwidth in nonparametric regression when errors have an almost arbitrarily long range of dependence. A novel analytical device for modelling the dependence structure of errors is introduced. This allows a concise theoretical description of the way in which the range of dependence affects optimal bandwidth choice. It is shown that, provided block length or leave-out number,…