We present a complete approach for simultaneous and automatic parameter estimation and image reconstruction which allows variable amounts of spatial smoothing. Procedures based on a Bayesian approach have been proposed, and successfully incorporate prior knowledge to produce much improved reconstructions. These procedures, however, usually assume that any prior parameters are known. In practice...

Damped trend exponential smoothing has previously been established as an important forecasting method. Here, it is shown to have close links to simple exponential smoothing with a smoothed error tracking signal. A special case of damped trend exponential smoothing emerges from our analysis, one that is more parsimonious because it effectively relies on one less parameter. This special case is c...

Spline smoothing provides a powerful tool for estimating nonparametric functions. Most of the past work is based on the assumption that the random errors are independent. Observations are often correlated in applications; e.g., time series data, spatial data and clustered data. It is well known that correlation greatly a ects the selection of smoothing parameters, which are critical to the perf...

A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate ...

In the first part of this paper we apply a saddle point theorem from convex analysis to show that various constrained minimization problems are equivalent to the problem of smoothing by spline functions. In particular, we show that near-interpolants are smoothing splines with weights that arise as Lagrange multipliers corresponding to the constraints in the problem of near-interpolation. In the...

in this paper, we review novel techniques in the emerging field of spatiotemporal 4d pet imaging. we will discuss existing limitations in conventional dynamic pet imaging which involves independent reconstruction of dynamic pet datasets. various approaches that seek to attempt some or all of these limitations are reviewed in this work, including techniques that utilize iterative temporal smooth...

In the statistical analysis of fMRI data, the parameter of primary interest is the effect of a contrast; of secondary interest is its standard error, and of tertiary interest is the standard error of this standard error, or equivalently, the degrees of freedom (df). In a ReML (Restricted Maximum Likelihood) analysis, we show how spatial smoothing of temporal autocorrelations increases the effec...

In this paper we use multiscale characteristics of wavelet decompositions and their relationship to smoothness spaces such as Besov spaces to derive a framework for smoothing and sharpening of signals and images. As a result, we derive a multiscale generalization of traditional techniques, such as unsharp masking, while using the smoothness parameter α in the Besov space Bα q (L p) to provide a...