Denoising 3D MR images by the enhanced non-local means filter for Rician noise

The non-local means (NLM) filter removes noise by calculating the weighted average of the pixels in the global area and shows superiority over existing local filter methods that only consider local neighbor pixels. This filter has been successfully extended from 2D images to 3D images and has been applied to denoising 3D magnetic resonance (MR) images. In this article, a novel filter based on the NLM filter is proposed to improve the denoising effect. Considering the characteristics of Rician noise in the MR images, denoising by the NLM filter is first performed on the squared magnitude images. Then, unbiased correcting is carried out to eliminate the biased deviation. When performing the NLM filter, the weight is calculated based on the Gaussian-filtered image to reduce the disturbance of the noise. The performance of this filter is evaluated by carrying out a qualitative and quantitative comparison of this method with three other filters, namely, the original NLM filter, the unbiased NLM (UNLM) filter and the Rician NLM (RNLM) filter. Experimental results demonstrate that the proposed filter achieves better denoising performance over the other filters being compared.     

Kolmogorov Averages and Approximate Identities

We study the action of Kolmogorov-type nonlinear averaging operators of the form V ⁻¹ AV on smooth functions. Here, A runs through a family of convolution operators A _ε ^[K], ε>0, generated by a single kernel K∈L ¹(ℝ ⁿ ) in the usual way and forming an “approximate identity” as ε→0, while V is a superposition map given by Vf=v○f, with a monotone continuous function v. The main result characterizes the kernels K with the property that the natural estimate

Cesàro Means of Orthogonal Expansions in Several Variables

Cesàro (C,δ) means are studied for orthogonal expansions with respect to the weight function on the unit sphere, and for the corresponding weight functions on the unit ball and the Jacobi weight on the simplex. A sharp pointwise estimate is established for the (C,δ) kernel with δ>−1 and for the kernel of the projection operator, which allows us to derive the exact order for the norm of the Cesàro means and the projection operator on these domains.      

On the two-dimensional Marcinkiewicz means with respect to Walsh–Kaczmarz system

In this paper we prove that the maximal operator of the Marcinkiewicz means of two-dimensional integrable functions with respect to the Walsh–Kaczmarz system is of weak type (1,1). Moreover, the Marcinkiewicz means converge to f almost everywhere, for any integrable function f.     

恒应力加速寿命试验中无失效数据的处理

对恒应力加速寿命试验中W eibu ll分布无失效数据,合理地构造了失效概率的两种先验分布,并结合现场试验数据,利用极大似然方法和Bayes方法对该组无失效数据进行了处理,所得结果表明本文给出的方法是正确可行的.     

Influence of noise and delay on reaction-diffusion recurrent neural networks

In this paper, the influence of the noise and delay upon the stability property of reaction-diffusion recurrent neural networks （RNNs） with the time-varying delay is discussed. The new and easily verifiable conditions to guarantee the mean value exponential stability of an equilibrium solution are derived. The rate of exponential convergence can be estimated by means of a simple computation based on these criteria.     

Bounds of the Hausdorff Measure of Sierpinski carpet

By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.     

Everywhere divergent Φ-means of Fourier series

For a function ? ∈, L ¹( $\mathbb{T}$ ), we investigate the sequence (C, 1) of mean values Φ(¦S _k (x, ?) ? ?(x)¦), where Φ(t): [0, +∞) → [0,+∞), Φ(0) = 0, is a continuous increasing function. We prove that if Φ increases faster than exponentially, then these means can diverge everywhere. Divergence almost everywhere of such means was established earlier.     

A nonparametric approach to 3D shape analysis from digital camera images — I

This article for the first time develops a nonparametric methodology for the analysis of projective shapes of configurations of landmarks on real 3D objects from their regular camera pictures. A fundamental result in computer vision, emulating the principle of human vision in space, claims that, generically, a finite 3D configuration of points can be retrieved from corresponding configurations in a pair of camera images, up to a projective transformation. Consequently, the projective shape of a 3D configuration can be retrieved from two of its planar views, and a projective shape analysis can be pursued from a sample of images. Projective shapes are here regarded as points on projective shape manifolds. Using large sample and nonparametric bootstrap methodology for extrinsic means on manifolds, one gives confidence regions and tests for the mean projective shape of a 3D configuration from its 2D camera images. Two examples are given: an example of testing for accuracy of a simple manufactured object using mean projective shape analysis, and a face identification example. Both examples are data driven based on landmark registration in digital images.     

常数磁场中薛定谔算子的黎斯平均的L2有界性估计

为了研究常数磁场下的薛定谔算子的黎斯平均L2有界性问题,本文在Stein研究的Fowrier变换的工作基础上,通过研究Mpf（x）,得到所要的估计.