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动态 PET 数据的非参数残留函数分析：健康受试者脑部 FDG 研究AI 解读

Kinetic analysis is used to extract metabolic information from dynamic positron emission tomography (PET) uptake data. The theory of indicator dilutions, developed in the seminal work of Meier and Zierler (1954), provides a probabilistic framework for representation of PET tracer uptake data in terms of a convolution between an arterial input function and a tissue residue. The residue is a scaled survival function associated with tracer residence in the tissue. Nonparametric…

正电子发射断层成像及广义反卷积模型的变异性评估AI 解读

The problem of variance assessment for positron emission tomography (PET) image reconstructions is considered in the context of generalized deconvolution. A refinement of an approximate technique proposed by Carson and colleagues is examined. Computational implications of representing the reconstruction kernel in terms of a weighted sum of Gaussian densities are developed. Bias and variance characteristics of the resulting variance estimators are examined by numerical…

正电子发射断层成像及广义反卷积模型的变异评估AI 解读

The problem of variance assessment for positron emission tomography (PET) image reconstructions is considered in the context of generalized deconvolution. A refinement of an approximate technique proposed by Carson and colleagues is examined. Computational implications of representing the reconstruction kernel in terms of a weighted sum of Gaussian densities are developed. Bias and variance characteristics of the resulting variance estimators are examined by numerical…

核不完全已知的反卷积及其在 FDG PET 血液曲线建模中的应用AI 解读

Camouflaged deconvolution arises when the kernel in a simple convolution model is not completely specified. We consider a situation in which the same fixed signal is repeatedly measured by separate convolutions with imprecisely known kernels. We develop a regularization methodology for application to these problems. The method involves simultaneous estimation of the target signal and the unknown parameters of the convolution kernels. Cross-validation is used to determine the…

卷积核未完全确定时的反卷积及其在 FDG PET 血液曲线建模中的应用AI 解读

Camouflaged deconvolution arises when the kernel in a simple convolution model is not completely specified. We consider a situation in which the same fixed signal is repeatedly measured by separate convolutions with imprecisely known kernels. We develop a regularization methodology for application to these problems. The method involves simultaneous estimation of the target signal and the unknown parameters of the convolution kernels. Cross-validation is used to determine the…

预测振荡模式：随机场时空分解方法的综合AI 解读

Spatial-temporal decompositions of climatologic fields have been obtained using a range of techniques, including principal component analysis (PCA) and principal oscillation patterns (POPS). PCA decompositions are forced to be correlated to the original field, but they may not capture interesting aspects of temporal variation. On the other hand, POPS decompositions focus on temporal variation but are not forced to correlate to the field. Here we introduce a hybrid of these…

预测振荡模式：随机场时空分解方法的综合AI 解读

Spatial-temporal decompositions of climatologic fields have been obtained using a range of techniques, including principal component analysis (PCA) and principal oscillation patterns (POPS). PCA decompositions are forced to be correlated to the original field, but they may not capture interesting aspects of temporal variation. On the other hand, POPS decompositions focus on temporal variation but are not forced to correlate to the field. Here we introduce a hybrid of these…

基于受扰直方图数据的间接密度估计带宽选择AI 解读

Motivated by a number of practical applications, we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts. Due to variability in the process of correction, the histogram cannot be modeled in terms of simple scaled Poisson statistics. This departure necessitates the development of a new methodology for bandwidth selection. A variant of the method of unbiased risk…

基于受扰直方图数据的间接密度估计带宽选择AI 解读

Motivated by a number of practical applications, we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts. Due to variability in the process of correction, the histogram cannot be modeled in terms of simple scaled Poisson statistics. This departure necessitates the development of a new methodology for bandwidth selection. A variant of the method of unbiased risk…

正电子发射断层成像重建中的最小二乘与最大似然比较AI 解读

Positron emission tomography (PET) is a radiologic tool offering a unique capability for measuring tissue metabolism in vivo. A number of biological and physical factors limit the resolution of PET so often the statistical aspects of image reconstruction have an appreciable effect on the quality of information obtained from a study. To a first approximation, reconstruction involves the solution of a linear inverse problem with a line-integral Radon-type transform. Standard…

基于惩罚 Whittle 似然的非参数谱密度估计AI 解读

The penalized likelihood approach is not well developed in time series analysis, even though it has been applied successfully in a number of nonparametric function estimation problems. Chow and Grenander proposed a penalized likelihood-type approach to the nonparametric estimation of the spectral density of Gaussian processes. In this article this estimator is extended to more general stationary processes, its practical implementation is developed in some detail, and some…

Cox 模型中的非参数估计AI 解读

Nonparametric estimation of the relative risk in a generalized Cox model with multivariate time dependent covariates is considered. Estimation is based on a penalized partial likelihood. Using techniques from Andersen and Gill, and Cox and O'Sullivan, upper bounds on rate of convergence in a variety of norms are obtained. These upper bounds match the optimal rates available for linear nonparametric regression and density estimation. The results are uniform in the smoothing…

通过层析成像进行多维密度估计AI 解读

SUMMARY The paper explores the application of the filtered backprojection algorithm of computerized tomography to statistical smoothing of multidimensional densities. The method makes use of automated one-dimensional density smoothers to obtain an automated smoothed multidimensional density. No structural assumptions such as additivity or log-additivity are used. An important computational aspect of this method is its inherently parallel structure. We demonstrate linear…

利用傅里叶方法进行离散拉普拉斯平滑AI 解读

An approach to multidimensional smoothing is introduced that is based on a penalized likelihood with a modified discretized Laplacian penalty term. The choice of penalty simplifies computational difficulties associated with standard multidimensional Laplacian smoothing methods yet without compromising mean squared error characteristics, at least on the interior of the region of interest. For linear smoothing in hyper-rectangular domains, which has wide application in image…

惩罚似然及相关估计量的渐近分析AI 解读

A general approach to the first order asymptotic analysis of penalized likelihood and related estimators is described. The method gives expansions for the systematic and random error. Asymptotic convergence rates in a family of spectral norms are obtained. The theory applies to a broad range of function estimation problems including nonparametric density, hazard and generalized regression curve estimation. Some examples are provided.

二维拉普拉斯平滑的迭代方法及其图像修复应用AI 解读

Smoothing methods are increasingly important in modern graphically oriented data analysis. There are several fast and reliable univariate cross-validated smoothing algorithms, but comparable methods are not available in higher dimensions. This article develops an iterative approach to two-dimensional Laplacian spline smoothing based on tensor-product cubic B splines. Estimating equations are developed and solved iteratively using two-line symmetric successive over relaxation…

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广义线性模型中回归函数的自动平滑AI 解读

We consider the penalized likelihood method for estimating nonparametric regression functions in generalized linear models (Nelder and Wedderburn 1972) and present a generalized cross-validation procedure for empirically assessing an appropriate amount of smoothing in these estimates. Asymptotic arguments and numerical simulations are used to show that the generalized cross-validatory procedure preforms well from the point of view of a weighted mean squared error criterion.…