Efficient anisotropic filtering of diffusion tensor images

To improve the accuracy of structural and architectural characterization of living tissue with diffusion tensor imaging, an efficient smoothing algorithm is presented for reducing noise in diffusion tensor images. The algorithm is based on anisotropic diffusion filtering, which allows both image detail preservation and noise reduction. However, traditional numerical schemes for anisotropic filtering have the drawback of inefficiency and inaccuracy due to their poor stability and first order time accuracy. To address this, an unconditionally stable and second order time accuracy semi-implicit Craig-Sneyd scheme is adapted in our anisotropic filtering. By using large step size, unconditional stability allows this scheme to take much fewer iterations and thus less computation time than the explicit scheme to achieve a certain degree of smoothing. Second-order time accuracy makes the algorithm reduce noise more effectively than a first order scheme with the same total iteration time. Both the efficiency and effectiveness are quantitatively evaluated based on synthetic and in vivo human brain diffusion tensor images, and these tests demonstrate that our algorithm is an efficient and effective tool for denoising diffusion tensor images.     

多孔材料分形扩散模型的Fourier-Bessel级数算法及其应用

将Fick扩散定律的Fourier三角级数算法推广成多孔材料分形扩散模型的Fourier-Bessel级数算法,并把它应用于化学工程中吸附问题涉及的浓度分布与相对吸附量的计算中,取得一些规律性认识.由于分形扩散模型是在Fick扩散定律的基础上增加了表征微观结构的参数d_f和θ,研究多孔材料中的浓度分布与相对吸附量时,与Fick扩散定律的研究结果相比,定性上基本一致,在定量上有差别,d_f和θ对扩散传质过程的影响各有侧重,用它们可更好地描述多孔材料中的扩散过程.     

Security Analysis of the Image Encryption Algorithm Based on a Two-Dimensional Infinite Collapse Map

This paper analyzes the security of the image encryption algorithm based on a two-dimensional (2D) infinite collapse map. The encryption algorithm adopts a permutation–diffusion structure and can perform two or more rounds to achieve a higher level of security. By cryptanalysis, it is found that the original diffusion process can be split into a permutation–diffusion structure, which comes after the original permutation, so these two permutations can be merged into one. Then, some theorems about round-down operation are summarized, and the encryption and decryption equations in the diffusion process are deduced and simplified accordingly. Since the chaotic sequences used in encryption algorithm are independent of the plaintext and ciphertext, there are equivalent keys. The original encryption algorithm with single-round, two-round, and multi-round of permutation–diffusion processes is cracked, and the data complexity of the cryptanalysis attacks is analyzed. Numerical simulation is carried out by MATLAB, and the experimental results and theoretical analysis show the effectiveness of the cryptanalysis attacks. Finally, some suggestions for improvement are given to overcome the shortcomings of the original encryption algorithm.     

改进的基于各向异性扩散的B超图像降噪方法

散斑噪声是超声成像机制引起的固有形态,它对超声图像质量以及医学诊断的准确性有很大的影响。针对传统Perona-Malik(PM)各向异性扩散模型通过四方向扩散无法提供充分的信息且处理效果不明显的问题,提出八方向选择式扩散模型;针对传统算法对强噪声则失效、扩散门限参数K依据经验选取的不足以及迭代终止条件不明确,提出改进的扩散系数计算方法,应用自适应选取的扩散门限参数K,且提出适合改进算法适用的迭代终止准则。经过多组仿真实验,证明本文算法较传统模型可以更好的控制扩散过程,并且提高了算法鲁棒性和效率,综合峰值信噪比(PSNR)、边缘保持度(FOM)等指标,表明该算法相比同类算法有更好的降噪和边缘保持效果。     

An Image Encryption Algorithm Based on Complex Network Scrambling and Multi-Directional Diffusion

Various security threats are encountered when keys are transmitted in public channels. In this paper, we propose an image encryption algorithm based on complex network scrambling and multi-directional diffusion. Combining the idea of public key cryptography, the RSA algorithm is used to encrypt the key related to plaintext. The algorithm consists of three stages: key generation stage, complex network scrambling stage, and multi-directional diffusion stage. Firstly, during the key generation phase, SHA-512 and the original image are used to generate plaintext-related information, which is then converted to plaintext-related key through transformation mapping. Secondly, in the complex network scrambling stage, the chaotic random matrix establishes the node relationships in the complex network, which is then used to construct an image model based on the complex network, and then combines pixel-level and block-level methods to scramble images. Finally, in the multi-directional diffusion stage, the multi-directional diffusion method is used to perform forward diffusion, middle spiral diffusion, and backward diffusion on the image in turn to obtain the final ciphertext image. The experimental results show that our encryption algorithm has a large keyspace, the encrypted image has strong randomness and robustness, and can effectively resist brute force attack, statistical attack, and differential attack.     

On some applications of diffusion processes for image processing

We propose a new algorithm inspired by the properties of diffusion processes for image filtering. We show that purely nonlinear diffusion processes ruled by Fisher equation allows contrast enhancement and noise filtering, but involves a blurry image. By contrast, anisotropic diffusion, described by Perona and Malik algorithm, allows noise filtering and preserves the edges. We show that combining the properties of anisotropic diffusion with those of nonlinear diffusion provides a better processing tool which enables noise filtering, contrast enhancement and edge preserving.     

Investigation of protein mass transfer by real-time holographic interferometry

Based on holographic interferometry data for electrophoresis and diffusion, an algorithm for quantitatively analyzing protein mass transfer in gels is suggested and implemented. The diffusion coefficients of a number of proteins in different media are found.     

Security Analysis and Improvement of an Image Encryption Cryptosystem Based on Bit Plane Extraction and Multi Chaos

This paper analyzes the security of image encryption systems based on bit plane extraction and multi chaos. It includes a bit-level permutation for high, 4-bit planes and bit-wise XOR diffusion, and finds that the key streams in the permutation and diffusion phases are independent of the plaintext image. Therefore, the equivalent diffusion key and the equivalent permutation key can be recovered by the chosen-plaintext attack method, in which only two special plaintext images and their corresponding cipher images are used. The effectiveness and feasibility of the proposed attack algorithm is verified by a MATLAB 2015b simulation. In the experiment, all the key streams in the original algorithm are cracked through two special plaintext images and their corresponding ciphertext images. In addition, an improved algorithm is proposed. In the improved algorithm, the generation of a random sequence is related to ciphertext, which makes the encryption algorithm have the encryption effect of a “one time pad”. The encryption effect of the improved algorithm is better than that of the original encryption algorithm in the aspects of information entropy, ciphertext correlation analysis and ciphertext sensitivity analysis.     

基于小波域扩散滤波的弱小目标检测

分析了基于小波变换进行弱小目标检测的基本思想,利用小波变换的多尺度多分辨率特性,结合小波变换系数的方向特性和扩散滤波扩散方向的可选择性,提出了基于小波域扩散滤波的弱小目标检测算法。采用该算法对不同尺度、不同方向的小波系数分别进行扩散滤波,取得了较好的效果。仿真试验结果表明：该算法能在Gaussian噪声背景和不均匀背景下实现对对比度为2%的微弱目标的检测。     

相位编码光学加密算法的扩散及混淆特性分析

为了阐明相位编码光学加密算法的扩散及混淆特性,基于傅里叶变换位移定理,从分组密码设计准则出发,以双随机相位光学加密算法为研究对象,分析了采用单个随机相位模板的2 f系统的扩散和混淆特性。将单随机相位加密过程分解为2个相互关联的过程,结果表明,傅里叶变换在加密算法中引入了混淆操作,而傅里叶变换结合随机相位模板实现了扩散操作。通过数值模拟对上述理论分析进行了验证,引入信息熵来评价加密图像的统计分布特性,进一步分析了菲涅尔域及分数阶傅里叶变换域随机相位加密算法的扩散混淆特性。研究表明,单随机相位加密和双随机相位加密图像的信息熵分布为7.038和7.157,而随机振幅加密图像信息熵为4.521。因而,随机相位加密算法比随机振幅加密算法能实现对信息更好地扩散。     

On the error diffusion algorithm: Object dependence of the quantization noise

Error diffusion is an important quantization algorithm suited for images as well as hologram distributions. A well known attribute of the algorithm is an inherent edge enhancement caused by a component of the quantization noise linearly dependent on the object distribution. One mechanism which causes the linear object dependent component is presented and the strength of the component is predicted analytically and verified experimentally for special selections of the free parameters of the error diffusion algorithm.     

Conductivity exponent in three-dimensional percolation by diffusion based on molecular trajectory algorithm and blind-ant rules

Diffusion on random systems above and at their percolation threshold in three dimensions is carried out by a molecular trajectory method and a simple lattice random walk method, respectively. The classical regimes of diffusion on percolation near the threshold are observed in our simulations by both methods. Our Monte Carlo simulations by the simple lattice random walk method give the conductivity exponent μ/ν=2.32±0.02 for diffusion on the incipient infinite clusters and μ/ν=2.21±0.03 for diffusion on a percolating lattice above the threshold. However, while diffusion is performed by the molecular trajectory algorithm either on the incipient infinite clusters or on a percolating lattice above the threshold, the result is found to be μ/ν=2.26±0.02. In addition, it takes less time step for diffusion based on the molecular trajectory algorithm to reach the asymptotic limit comparing with the simple lattice random walk.     

Saliency detection based on diffusion maps

Visual saliency has recently attracted lots of research interest in the computer vision community. In this paper, we propose a novel computational model for bottom-up saliency detection based on manifold learning. A typical graph-based manifold learning algorithm, namely the diffusion maps, is adopted for establishing our saliency model. In the proposed method, firstly, a graph is constructed using low-level image features. Then, the diffusion maps algorithm is performed to learn the diffusion distances at different time, which are utilized to derive the saliency measure. Compared to existing saliency models, our method has the advantage of being able to capture the intrinsic nonlinear structures in the original feature space. Experimental results on publicly available data demonstrate that our method outperforms the state-of-the-art saliency models, both qualitatively and quantitatively.     

A phase-field/Monte-Carlo model describing organic crystal growth from solution

In this paper work we present a phase-field/Monte-Carlo hybrid algorithm for the simulation of solutal growth of organic crystals. The algorithm is subsequently used for an investigation of diffusion effects on the growth mechanisms. This method combines a two-scale phase-field model of the liquid phase epitaxial growth and a Monte-Carlo algorithm of the 2D nucleation and thus is faster than previous purely Monte Carlo simulations of crystal growth. The inclusion of supersaturation and diffusion in the method allows the study of crystal growth under various growth conditions. Parameters used in the hybrid algorithm are bound to the energetic parameters of crystal faces, which can be estimated from a detailed study of the actual crystal structure based on a connected nets analysis, which allows the prediction of the shape and morphology of real crystals. The study of the diffusion effect is carried out based on an example of a hydroquinone crystal, which grows from the water solution at various supersaturations. The dependencies of the growth rate and the nucleation rate on the supersaturation indicate the change of the growth mechanism from spiral growth to 2D nucleation. The difference in the growth rate for various faces is in agreement with the crystal morphologies derived from the attachment energy method and observed experimentally. The main result of the simulation is the evaluation of engineering limits for choosing appropriate external process conditions.     

Temporal information effect on personalized recommendation

As information explosively grows, it requires to find out the highly efficient data from the global database. In this paper, based on two real systems, i.e., the MovieLens and Netflix, we investigate the temporal information effect on personalized recommendation for three collaborative filtering algorithms, by considering both the volume and time of the training data. It is observed that, for an increasing training data of a certain time range, the recommendation accuracy using the time-dependent training data outperforms that using the random training data of the same size. Moreover, the increase of data volume would not always improve the recommendation accuracy for the time-dependent training data case, whereas the recent temporal training data are important to elevate the recommendation accuracy. Further study on a hybrid algorithm of heat conduction and mass diffusion shows that, using the recent temporal information as training data, the algorithm reaches the optimal recommendation accuracy, when it returns to the original mass diffusion algorithm, which suggests no necessity of introducing an extra parameter. And the simple mass diffusion algorithm is found to be more advantageous than the previous three algorithms.     

Application of the Nuclear Reaction Analysis Online Technique to Study the Diffusion of Deuterium in Metals

Nuclear reaction analysis online technique has been applied to study the diffusion of deuterium in metals. Investigations ensuring the application of the new method have been performed. These investigations include the development of a device for diffusion annealing of samples in the chamber of an accelerator and an algorithm for taking into account the effect of radiation defects on the diffusion coefficients. Test measurements of the diffusion coefficients of deuterium in nickel in the temperature range from 130 to–60°С have been performed. For negative temperatures, experimental data on the diffusion of a hydrogen isotope in a metal have been obtained for the first time by a direct method and it has been shown that the online nuclear reaction analysis provides reliable data.     

An efficient and accurate reconstruction algorithm for the formulation of cell-centered diffusion schemes

A new reconstruction algorithm is proposed for constructing cell-centered diffusion schemes on distorted meshes. Its main feature is that edge unknowns are defined at certain balance points, the locations of which depend on the diffusion coefficient and the skewness of grid cells, so as to obtain a two-point reconstruction stencil. Implementing the new algorithm for the approximation of gradients, we extend the IDC (improved deferred correction) scheme, which was proposed by Traoré et al. [P. Traoré, Y. Ahipo, C. Louste, A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries, J. Comput. Phys. 228 (2009) 5148–5159], to handle diffusion problems with discontinuous coefficients. Numerical results demonstrate the accuracy and efficiency of the extended scheme.     

基于小波域扩散滤波的弱小目标检测

分析了基于小波变换进行弱小目标检测的基本思想,利用小波变换的多尺度多分辨率特性,结合小波变换系数的方向特性和扩散滤波扩散方向的可选择性,提出了基于小波域扩散滤波的弱小目标检测算法。采用该算法对不同尺度、不同方向的小波系数分别进行扩散滤波,取得了较好的效果。仿真试验结果表明:该算法能在Gaussian噪声背景和不均匀背景下实现对对比度为2%的微弱目标的检测。     

光学相干层析图像层状结构的增强与定量测量

光学相干层析(OCT)成像技术对于眼底等层状组织的定量测量有赖于光学相干层析图像中层状结构的提取。为了对原始光学相干层析图像进行预处理以有效地去除图像中的噪声及散斑、增强图中的层状结构,并更好地保护图像中的层状结构,进而更准确地定量测量图像中有重要意义的层状结构的光程信息,提出在相干增强各向异性扩散(CED)算法中引入二阶导数项以控制沿相干方向的扩散强度,并将引入二阶导数项的相干增强各向异性扩散算法应用于不同样品的光学相干层析图像。结合在预处理后图像中层状结构位置的查找结果与样品的折射率信息,实现了对光学相干层析图像中有重要意义的层状结构厚度的定量测量。实验结果表明,使用引入二阶导数项的相干增强各向异性扩散算法对光学相干层析图像预处理有利于对图中重要层状结构的更准确测量。     

MRI diffusion tensor reconstruction with PROPELLER data acquisition

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.