High-order total variation-based Poissonian image deconvolution with spatially adapted regularization parameter

Images captured by image acquisition systems using photon-counting devices such as astronomical imaging, positron emission tomography and confocal microscopy imaging, are often contaminated by Poisson noise. Total variation (TV) regularization, which is a classic regularization technique in image restoration, is well-known for recovering sharp edges of an image. Since the regularization parameter is important for a good recovery, Chen and Cheng (2012) proposed an effective TV-based Poissonian image deblurring model with a spatially adapted regularization parameter. However, it has drawbacks since the TV regularization produces staircase artifacts. In this paper, in order to remedy the shortcoming of TV of their model, we introduce an extra high-order total variation (HTV) regularization term. Furthermore, to balance the trade-off between edges and the smooth regions in the images, we also incorporate a weighting parameter to discriminate the TV and the HTV penalty. The proposed model is solved by an iterative algorithm under the framework of the well-known alternating direction method of multipliers. Our numerical results demonstrate the effectiveness and efficiency of the proposed method, in terms of signal-to-noise ratio (SNR) and relative error (RelRrr).     

相依误差广义线性模型的M估计的Bahadur表示

考虑如下广义线性模型y_i=h(x~T_i,β)+e_i=1,2,…,n,其中e_i=G(…,ε_(i-1),ε_i),h是一个连续可导函数,ε_i是独立同分布的随机变量,并且它的期望为0,方差σ~2有限.本文给出了参数β的M估计,并且得到了该估计的Bahadur表示,该结论推广了线性模型的相关结论.应用M估计的Bahadur表示,得到了相依误差的线性回归模型,poisson模型,logistic模型和独立误差的广义线性模型等模型的渐近性质.     

限制pre-李代数

研究限制pre-李代数的结构,给出了限制pre-李代数和可限制pre-李代数的定义,得到了限制pre-李代数的p-映射性质和可限制pre-李代数的性质,还讨论了带有半单元的限制pre-李代数及拟环面限制pre-李代数和分解唯一性定理.     

用指数型整函数的最佳限制逼近

我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果.     

自由Rota-Baxter代数的因子分解

近年来,Rota-Baxter代数在数学和物理学中有着广泛的应用,受到越来越多的关注,自由Rota-Baxter代数分别用括号字,根树以及Motzkin路径得到了构造.因子分解在代数学中是一个很重要的问题.本文主要考虑用括号字构造的自由RotaBaxter代数,得到了自由Rota-Baxter代数中基元素的因子分解.     

具有N-各向异性拉普拉斯算子的超线性问题的先验界

通过改进Brezis和Merle的方法,结合Moser-Trudinger不等式,移动平面方法及比较原理,得到了方程-Q_Nu=f(u),u∈W_0~(1,N)(Ω)的正解的先验界,其中Ω是R~N中的一个有界光滑区域,非线性项f至多具有指数型增长.     

M-矩阵线性互补问题模系多分裂迭代方法的收敛性

首先证明了M-矩阵的H-相容分裂都是正则分裂,反之不成立.这表明对于M-矩阵而言,其正则分裂包含H-相容分裂.然后针对系数矩阵为M-矩阵的线性互补问题,建立了两个收敛定理:一是模系多分裂迭代方法关于正则分裂的收敛定理;二是模系二级多分裂迭代方法关于外迭代为正则分裂和内迭代为弱正则分裂的收敛定理.     

Multi-poly-Bernoulli numbers and polynomials with a <Emphasis Type="Italic">q</Emphasis> parameter

We introduce themulti-poly-Bernoulli numbers and polynomialswith a q parameter, which are generalizations of the poly-Bernoulli numbers and polynomials with a q parameter, respectively.We give several combinatorial identities and properties of these new numbers and polynomials.