拉普拉斯约束低秩表示的高光谱图像异常检测

伴随高光谱图像的广泛使用,高光谱图像技术得到长足的发展,其中高光谱图像异常检测技术越发受到重视。为了解决传统高光谱图像异常检测技术的实用性和检测效果不佳的问题,提出一种新颖的低秩表示检测算法。对于高光谱图像,大部分背景像元均可以被少量主要的背景像元组合近似地表示,且它们的表示系数将会位于低秩的空间中。在剩下无法被主要背景像元表示的稀疏部分中存在着异常像元,则可以被检测算法提取出来。在低秩表示中,背景像元字典的构建将会影响高光谱图像中背景像元的表示。如直接从现有高光谱图像中提取背景像元构建字典,会导致异常像元对背景像元字典的污染。而利用待检测高光谱图像观测数据和由光谱组成原理可合成的潜在未观测数据来构建背景像元字典,提取出背景像元的主要特征,有利于更好地分离出稀疏异常像元的信息。并且高光谱图像数据存在高维几何结构特点,通过引入拉普拉斯矩阵来约束空间中局部相似的像元对于待检测像元的表示作用,获得更接近于真实的表示系数。实验结果分别在仿真数据和真实数据上验证,与传统方法相比,提出的方法通过有效地突出异常像元提高了检出率和抑制了背景像元,降低了误检率。     

Complex Hyperspherical Equations, Nodal-Partitioning, and First-Excited-State Theorems in ℝ n

Three problems related to the spherical quantum billiard in are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in . The second topic addresses the first-excited-state theorem for the spherical quantum billiard in . Wavefunctions for this system are given by the product form, ( )Z _q+()Y ⁽ⁿ⁾ , where is dimensionless displacement, is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written . It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in . In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in by enumerating independent degenerate product eigenstates of the Laplacian.     

Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization

Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges.     

Coherent orthogonal polynomials

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. II. Extended Results for Square-Lattice Chromatic Polynomial

We study the chromatic polynomials for m×n square-lattice strips, of width 9m13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.     

奇偶对相干态的维格纳函数和层析图函数

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数.根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应.研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质.奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著.利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,τ1,τ2〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数.     

Quantum Phase Transition in Quasi-two-dimensional Heisenberg Antiferromagnet with Single-Ion Anisotropy

In the present paper, we investigate the quantum phase transition in a spatially anisotropic antiferrornagnetic Heisenberg model of S =1 with single-ion energy anisotropy. By using the Schwinger boson representation, we calculate the Gaussian correction to the critical value J⊥^c caused by quantum spin fluctuations. We find that, for the positive single-ion energy, a nonzero value of J⊥^c is always needed to stabilize the antiferromagnetic long-range order in this model. It resolves a difference among literature and shows clearly that the effect of quantum fluctuations may qualitatively change a result obtained by the mean-field theories on lower-dimensional systems.     

Some analytical aspects in field theories with dynamical mass generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looked for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand in hand with the nontrivial solution for mass function. The consequences are discussed.