Bootstrap bandwidth selection in kernel density estimation from a contaminated sample

In this paper we consider kernel estimation of a density when the data are contaminated by random noise. More specifically we deal with the problem of how to choose the bandwidth parameter in practice. A theoretical optimal bandwidth is defined as the minimizer of the mean integrated squared error. We propose a bootstrap procedure to estimate this optimal bandwidth, and show its consistency. These results remain valid for the case of no measurement error, and hence also summarize part of the theory of bootstrap bandwidth selection in ordinary kernel density estimation. The finite sample performance of the proposed bootstrap selection procedure is demonstrated with a simulation study. An application to a real data example illustrates the use of the method. This research was supported by ‘Projet d’Actions de Recherche Concertées’ (No. 98/03-217) from the Belgian government. Financial support from the IAP research network nr P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) is also gratefully acknowledged.     

Kullback-Liebler测度在地震记录反演中的应用

在地震记录反演中,盲目反褶积是一个相当困难的问题.讨论这个问题现有各种方法,如累积矩法等.本文利用Likas等处理图像恢复的变分法来讨论地震记录反演中的盲目反褶积问题.利用Kullback-Liebler信息测度获得一个非常有用的统计函数(即变分函数),此函数的极值点就含有所要求的反射系数序列的信息,并且拟订出求此泛数极值点的一套算法.     

Motion blur parameters estimation for image restoration

This paper deals with estimation of parameters for motion blurred images. The objectives are to estimate the length (L) and the blur angle (θ) of the given degraded image as accurately as possible so that the restoration performance can be optimised. Gabor filter is utilized to estimate the blur angle whereas a trained radial basis function neural network (RBFNN) estimates the blur length. Once these parameters are estimated the conventional restoration is performed. To validate the proposed scheme, simulation has been carried out on standard images as well as in real images subjected to different blur angles and lengths. The robustness of the scheme is also validated in noise situations of different strengths. In all situations, the results have been compared with standard schemes. It is in general observed that the proposed scheme outperforms its counterparts in terms of restoration parameters and visual quality.     

Two-stage blind deconvolution scheme using useful priors

Hand shake blurry image is a common phenomenon in our daily life. In this paper, a novel blind deconvolution scheme is proposed to recover a single hand shake blurry image. The algorithm is subdivided into two main stages, kernel estimation stage and non-blind deconvolution stage. In the kernel estimation stage, we propose a cost function taking a selected map into consideration. In the non-blind decovolution stage, another cost function is designed using image derivatives prior. We also present an adaptive kernel size selection method instead of traditional manual selection. Extensive experiments on real world blurry images are conducted to demonstrate the performance of our algorithm.     

Metamictization in zircon. Part I: Raman investigation following a Rietveld approach: Profile line deconvolution technique.

The line profile form of Raman spectra can be analyzed using the very same approach and software used for diffractogram deconvolution via the Rietveld approach. In both cases the ‘true’ profile containing information about the sample must be separated from the instrument's profile function (and potentially from the emission profile) which can be achieved by deconvolution. In this first part of a two‐part study we demonstrate how the instrument's function can be described via a Gaussian function profile (yielding the very same result as several convoluted hat functions) using several examples (diamond, calcite, silicon and silicon carbide) for which true Raman bandwidth values are presented (assuming the true band profile to be Lorentzian). Also, asymmetrical bands can be described and analyzed via the presented deconvolution approach. The second part of this study will discuss and apply this method for studying the radiation‐induced damage in zircon grains (metamictization). Copyright © 2008 John Wiley & Sons, Ltd.     

最近邻域与无邻域算法结合空间滤波实现显微光切片

运用最近邻域与无邻域算法,并结合空间滤波方法,可去除显微切层图像的离焦模糊成份,可获得高成像速度、高质量的显微光切片。对各种显微图像进行了光切片处理,并与由现有去卷积处理、结构光照明等方法获得的光切片图像进行了对比,验证了该算法在去除模糊信息方面有更好的效果,提高了图像处理效率,获得了令人满意的光切片图像。在此基础上研制出了显微光切片图像处理系统。运用最近邻与无最近邻算法,结合空间滤波方法,采用简便可调的卷积模糊算子代替点扩散函数的估计过程,图像处理方便快捷,可较好地去除离焦平面的模糊信息。     

Iterative Wiener deconvolution based method for phase retrieval from noisy intensities

To retrieve the phase from the noisy measured intensities in the diffraction planes, an iterative Wiener deconvolution based method is proposed. With the same iterative scheme as the iterative angular spectrum method (IAS), the propagation of the optical wave function between the input plane and the diffraction planes is calculated by Wiener deconvolution in this method. The angular spectrum convolution kernel used in the iterative angular spectrum method is incorporated into the Wiener filter. The simulation experiments show that the proposed method can reduce the impact of the noise on the retrieved phase and performed better than the pre-denoising method. Furthermore, the proposed method exhibits great advantage compared to IAS for retrieving the complicated phase distribution from two measured intensities.     

Chromatographic Chiral Recognition and Computer Aided Deconvolution of the Enantiomeric Secondary Alcohol with a Self‐Packed Chiral Stationary Phase HPLC Column

The γ‐aminopropyl‐derivatized silica was treated with the (R)‐(‐)‐N‐(3,5‐dinitrobenzoyl)‐α‐phenylglycine and was packed into a standard 250 mm × 4.5 mm HPLC column to perform the chiral separation of secondary alcohol. Enantiomers of four homologous series of aryl alkyl substituted alcohol were resolved in different degrees. The chiral recognition mechanism was proposed that could be used to rationalize well the elution order and the resolution between the R‐ and S‐configuration of a secondary alcohol. The unresolved peak of the enantiomers of 1‐phenylethanol and the partially resolved peak of the enantiomers of 1‐(1‐naphthyl)ethanol were deconvoluted by the assistance of computer and a program written in BASIC computer language. Two mathematical models were used for the deconvolution and were based on modified Gaussian functions with a fixed baseline that can take into account the skew of a chromatographic peak. Parameters in the mathematical model were estimated by using a nonlinear regression algorithm. The selected mathematical models were suitable for deconvolving the less skewed overlapping peaks of 1‐phenylethanol.     

Application of multi-frame approach in single-frame blind deconvolution

A new single-frame blind deconvolution algorithm for the linear shift-invariant imaging system is presented. The algorithm processes the partial images segmented from one single degraded image by multi-frame approach to recover the point spread function (PSF). Then a deconvolution method is employed to restore the whole image with the recovered PSF. In addition, in order to improve the fidelity and resolution of the recovered PSF, the coprimeness of the partial images is utilized. Results of simulated and real atmospheric turbulence degraded images using the algorithm are reported.     

Determination of the fluorescence lifetime of glyoxal(C_2H_2O_2)water solution by beconvolution

This paper reports that the actual fluorescence lifetime 7.64±0.06ns of a10％-glyoxal water solution is determined for the first time from the laser-induced fluores-cence decay curve detected by the system with a response time in the order of magnitude ofnanosecond and processed by deconvolution on combination with phase plane method and iter-ative convolution method.The experimental method presented in this paper is regarded as aneffective method for measuring the fluorescence lifetime in nanoseconds or even in sub-nanoseconds by means of a detecting system with an order of magnitude of nanosecond.