Inverse subspace problems with applications

Given a square matrix A, the inverse subspace problem is concerned with determining a closest matrix to A with a prescribed invariant subspace. When A is Hermitian, the closest matrix may be required to be Hermitian. We measure distance in the Frobenius norm and discuss applications to Krylov subspace methods for the solution of large‐scale linear systems of equations and eigenvalue problems as well as to the construction of blurring matrices. Extensions that allow the matrix A to be rectangular and applications to Lanczos bidiagonalization, as well as to the recently proposed subspace‐restricted SVD method for the solution of linear discrete ill‐posed problems, also are considered.Copyright © 2013 John Wiley & Sons, Ltd.     

Diagonalization of tensors with circulant structure

The concepts of tensors with diagonal and circulant structure are defined and a framework is developed for the analysis of such tensors. It is shown a tensor of arbitrary order, which is circulant with respect to two particular modes, can be diagonalized in those modes by discrete Fourier transforms. This property can be used in the efficient solution of linear systems involving contractive products of tensors with circulant structure. Tensors with circulant structure occur in models for image blurring with periodic boundary conditions. It is shown that the new framework can be applied to such problems.     

联合梯度预测与导引滤波的图像运动模糊复原

针对由相机与所摄景物之间发生相对位置移动所导致的图像运动模糊,提出了一种鲁棒的基于单幅运动模糊图像的盲反卷积算法。该方法首先通过预测图像中的较强边缘信息,实现用简单、易于求解的优化问题在傅里叶域中快速、准确地估计出点扩散函数。然后利用得到的点扩散函数,使用基于梯度约束的非盲反卷积算法复原清晰图像,同时采用一种新的边缘保持滤波器-导引滤波来消除噪声并抑制振铃效应。实验结果表明：本文的算法能够快速地从单幅运动模糊图像复原出具有清晰边缘和纹理的高质量图像,并且运算时间不超过20 s。     

Relationship between the fringe number of the scanning beam and the twin-image noise

A method of digital filtering for eliminating the twin-image noise of reconstructed images in optical scanning holography is proposed and demonstrated by the example of slit objects. The fringe number of the scanning beam in relation to the twin-image noise is investigated in detail. Some results of computer simulations are obtained. In the far field, the further object scanned by the scanning beam with fewer fringes has lower and flatter amplitude of the twin-image noise for reconstructed images. However, being independent of the fringe number the twin-image noise affects seriously on the reconstruction in the near field. So the twin-image noise should be considered in reconstruction in the near field.     

Stability of the notion of approximating class of sequences and applications

Given an approximating class of sequences {{B_n,m}_n}_m for {A_n}_n, we prove that (X⁺ being the pseudo-inverse of Moore–Penrose) is an approximating class of sequences for , where {A_n}_n is a sparsely vanishing sequence of matrices A_n of size d_n with d_k>d_q for k>q,k,qN. As a consequence, we extend distributional spectral results on the algebra generated by Toeplitz sequences, by including the (pseudo) inversion operation, in the case where the sequences that are (pseudo) inverted are distributed as sparsely vanishing symbols. Applications to preconditioning and a potential use in image/signal restoration problems are presented.     

X射线衍射增强成像中的定量测量

提出了一种基于X射线衍射增强成像(DEI)断层计算机X射线层析术(CT)图像的物体尺寸精确测量方法.X射线衍射增强成像是一种基于相位衬度的成像技术.通过建立DEI的简化模型,研究衍射成像过程中品体转角、投影图像谷点位置、成像系统等效模糊等因素之间关系,由此具体探讨了系统模糊效应对圆物体边界成像带来的位置偏移,并以圆形被测样品为例.提出可精确测定直径的简单有效算法.通过理论仿真模型数据和北京同步辐射装置上的实测数据验证了该算法的精度.该方法实现了利用DEI图像对被测物体几何尺寸的精确测量,可用于对牛物组织样品等物体内部微小结构的尺寸的精确测量.     

A video-rate range sensor based on depth from defocus

Recovering the depth information derived from dynamic scenes implies real-time range estimation. This paper addresses the implementation of a bifocal range sensor which estimates the depth by measuring the relative blurring between two images captured with different focal settings. To recover the depth accurately even in cases when the scene is textureless, one possible solution is to project a structured light on the scene. As a consequence, in the scene's spectrum a spatial frequency derived from illumination pattern is evident. The resulting algorithm involves only simple local operations, this assures the possibility of computing the depth at a rate of 10 frames per second. The experimental results indicate that the accuracy of this proposed sensor compares well with that offered by other methods such as stereo and motion parallax, while avoiding the problems caused by occlusion and missing parts.     

基于指导滤波的图像盲复原算法

作为图像处理领域的重要分支和研究热点之一, 图像复原方法 的研究始终具有重要理论意义和广泛的应用价值, 图像盲复原一直以来都 是图像复原中比较困难的问题之一. 针对相机与所拍摄景物之间由于相对 位置移动而使所获得图像发生运动模糊的情况, 本文提出了一种基于指导滤波 的图像盲复原算法. 我们首先通过频域迭代算法对点扩散函数 进行估计. 然后, 由于指导滤波具有较好的保持图像边缘的特性, 我们应用基于指导滤波的图像非盲复原算法恢复目标图像. 对以上两步进行反复迭代, 直到获得最终的清晰图像. 为了验证本文所提算法的有效性, 给出了多组对比实验. 实验结果表明, 本文所提算法能够在有效地抑制噪声和振铃 效应的同时, 还能够更好的保持图像的边缘和纹理细节. 因此, 本文算法可以获得更高质量的复原图像.     

Image restoration of skin scattering and optical blurring for finger vein recognition

Finger vein recognition has been adopted due to its high recognition rate and the invisibility of vein in visible light. However, because a finger vein pattern is not distinctive due to light scattering in the skin layer, the localization of a finger vein pattern region using an image processing algorithm is a difficult procedure. Also, optical blurring increases these difficulties. We propose a new finger vein image restoration method to deal with skin scattering and optical blurring. Our research is novel in three ways compared to previous studies. Firstly, the amount of optical blurring of a finger vein image is measured based on the average gradient of the orthogonal profile of a finger edge. Secondly, the accurate point spread function (PSF) of optical blurring is adaptively determined based on the orthogonal profile of a finger edge. Thirdly, using a constrained least square (CLS) filter and optimized parameters in terms of the lowest error of finger vein recognition, the restoration of a skin scattered and optically blurred finger vein pattern was performed. Experimental results show that the equal error rate (EER) of finger vein recognition with restoration was reduced by as much as 3.14% (5.05-1.91%) compared to the EER without restoration.     

The influence of structure depth on image blurring of micrometres-thick specimens in MeV transmission electron imaging

This study investigates the influence of structure depth on image blurring of micrometres-thick films by experiment and simulation with a conventional transmission electron microscope (TEM). First, ultra-high-voltage electron microscope (ultra-HVEM) images of nanometer gold particles embedded in thick epoxy-resin films were acquired in the experiment and compared with simulated images. Then, variations of image blurring of gold particles at different depths were evaluated by calculating the particle diameter. The results showed that with a decrease in depth, image blurring increased. This depth-related property was more apparent for thicker specimens. Fortunately, larger particle depth involves less image blurring, even for a 10-μm-thick epoxy-resin film. The quality dependence on depth of a 3D reconstruction of particle structures in thick specimens was revealed by electron tomography. The evolution of image blurring with structure depth is determined mainly by multiple elastic scattering effects. Thick specimens of heavier materials produced more blurring due to a larger lateral spread of electrons after scattering from the structure. Nevertheless, increasing electron energy to 2 MeV can reduce blurring and produce an acceptable image quality for thick specimens in the TEM.