Double Smoothing Research Articles

Interlaced to progressive scan conversion with double smoothing

An interlaced to progressive (I/P) scan conversion scheme based on a three-point vertical median filtering is described. The three points are the interlaced data passed through double smoothing (DS). The DS based on order statistic filtering preceded by censoring eliminates impulsive and/or nonimpulsive noise while preserving signal edges. The three-point vertical median operation for I/P conversion controls the adaptive switching between a moving scene mode and a stationary scene mode without complex motion and edge detection. A structure for implementation of the proposed I/P conversion circuit is described. This circuit features an integrated dynamic RAM based on horizontal lines, a field memory, and a high-speed bubble sorter. Test results confirm that the proposed scheme is effective in I/P conversion for impulsive and/or nonimpulsive noise-contaminated images. >

Regression Smoothing Parameters that are not Far from their Optimum

Abstract It is well known that data-driven regression smoothing parameters ħ based on cross-validation and related methods exhibit a slow rate of convergence to their optimum. In an earlier article we showed that this rate can be as slow as n –1/10; that is, for a bandwidth ħ 0 optimizing the averaged squared error, n 1/10 (ħ — ħ 0)/ħ 0 tends to an asymptotic normal distribution. In this article we consider mean averaged squared error optimal bandwidths h 0. This (nonrandom) smoothing parameter can be approximated much faster. We use the technique of double smoothing to show that there is an ħ such that, under certain conditions, n 1/2(ħ − h 0)/h 0 tends to an asymptotic normal distribution.

Double smoothing for kernelestimators in nonparametric regression

For the random design nonparametric regression, we use the double smoothing technique to construct kernel estimators of the regression function and its derivatives. As an estimator of the regression function, this double smoothing estimator (DSE) shares the superior asymptotic variance quantity of the Nadaraya-Watson estimator (NWE) and the nice asymptotic bias quality of the Gasser-Mueller estimator (GME). Based on the asymptotic mean square error (AMSE), the DSE is uniformly better than the GME. To estimate derivatives of the regression function, the estimators derived by the DSE give insight directly and good interpretability, and are also uniformly better than those derived by the GME, in terms of the AMSE. Under the regularity conditions, these DSE of the regression function and its derivatives are asymptotically normal.

Double smoothing of images using median and Wiener filters

The authors propose double smoothers, consisting of the median and Wiener filters, which they call the median and Wiener (MW) double smoothers. It is shown that the MW double smoother is suitable for smoothing a covariance stationary process which is a useful model of images. The statistical analysis and experimental results indicate that the MW double smoother is an efficient edge-preserving smoother that can outperform the individual median and Wiener filters. >

AN EMPIRICAL EVALUATION OF INDIVIDUAL ITEM FORECASTING MODELS

A computer simulation experiment was replicated to correct errors in an earlier paper and to compare seven individual item forecasting models across five different demand patterns. Results confirm previous findings that the better forecasting model depends upon the demand pattern and the forecast horizon, as well as the noise level. Nevertheless, exponential double smoothing emerged as the most robust model.

Applications of a nonlinear smoothing algorithm to speech processing

In this paper a nonlinear smoothing algorithm recently proposed by Tukey is described and evaluated for speech processing applications. Simple linear smoothing routines generally fail to provide adequate smoothing for data which exhibit both local roughness and sharp discontinuities. The proposed nonlinear smoothing algorithm can effectively smooth such data by using a combination of median smoothing routines and linear filtering. The concept of double smoothing is introduced as a refinement on the smoothing algorithm. Examples of the application of the nonlinear smoothing methods to typical speech parameters are included in this paper.

Applications of nonlinear smoothing to speech processing

In this talk a simple nonlinear smoothing algorithm which is appropriate for many speech-processing applications is described and evaluated. In many applications linear smoothers, or low-pass filters are entirely adequate. However, simple linear smoothers generally fail to provide adequate smoothing for data which exhibit both local roughness and sharp discontinuities. The proposed nonlinear smoothing algorithm can effectively smooth such data by using a combination of median smoothing routines and linear filtering. The concept of double smoothing as a refinement on the smoothing algorithm is also discussed. Examples showing the application of the nonlinear smoothing methods to typical speech parameters are included in this talk.

INDIVIDUAL ITEM FORECASTING MODEL EVALUATION*

ABSTRACTA computer simulation experiment was conducted to evaluate and compare seven individual item forecasting models across five different demand patterns. Results indicate the best model varies depending upon the demand pattern, the time period forecast, the noise level of the demand pattern, and to a lesser extent the measure of forecast error. Across all demand patterns, exponential double smoothing was best for the long run forecast and at least second best for the short run regardless of noise level in the demand patterns. Analysis of models within a demand pattern yielded, in most cases, several models as ranking equally well. The adaptive model developed here did not perform as well as some other models. For example, it ranked no better than third on a step function demand pattern.