Modified Gerchberg–Saxton (G-S) Algorithm and Its Application

The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which n plaintexts can be recovered from n ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm.     

Dynamic optimization problems with bounded terminal conditions

Bounded terminal conditions of nonlinear optimization problems are converted to equality terminal conditions via the Valentine's device. In so doing, additional unknown parameters are introduced into the problem. The transformed problems can still be easily solved using the sequential gradient-restoration algorithm (SGRA) via a simple augmentation of the unknown parameter vector . Three example problems with bounded terminal conditions are solved to verify this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC 2-106.     

Numerical analysis for factorial data analysis. Part II: Special purpose hardware—the programmable systolic array SARDA

The second part of this paper deals with the systolic implementation of the computational kernel for factorial data analysis, defined in Part I, on special-purpose hardware. The framework of the study is that a sequence of different algorithms has to be performed on a unique hardware array. This fact has led us to the design of the programmable systolic array SARDA: this is a triangular array which consists of programmable nodes with local memory and programmable orthogonal connections.     

Sequential stopping rules for the multistart algorithm in global optimisation

In this paper a sequential stopping rule is developed for the Multistart algorithm. A statistical model for the values of the observed local maxima of an objective function is introduced in the framework of Bayesian non-parametric statistics. A suitablea-priori distribution is proposed which is general enough and which leads to computationally manageable expressions for thea-posteriori distribution. Sequential stopping rules of thek-step look-ahead kind are then explicitly derived, and their numerical effectiveness compared.     

A primal-dual algorithm for the fermat-weber problem involving mixed gauges

We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior and a counterexample to finite termination is given in a case where this property is violated. Finally, numerical results are reported and we discuss possible extensions of these results.     

Fourier acceleration of iterative processes in disordered systems

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.     

Pansystems studies in stability,bifurcation and chaos

This paper divides fixed subsets into three kinds, mainly discusses the existence of II-type fixed subset, connects the investigations infixed subsets with the studies in non-linear problems, such as stability, bifurcation, chaos, etc., and proposes a kind of discrete simulation to Liapunov stability and his second method.     

Banach空间中关于(H,η)增生算子的变分包含问题

在Banach空间中引进了一类(H,η)增生算子,利用预解算子技巧,建立了一个Ishikawa迭代,并证明了此迭代算法产生的变分包含的解的存在与唯一性。其结果是近期相关结果的改进与推广。     

高速SHA-256算法硬件实现

SHA-256安全散列算法在数字加密、数字签名中被广泛应用．为满足应用对算法运算速度的要求,提出一种快速实现SHA-256安全散列算法的的硬件新结构．方法通过对算法进行推导,使得能在硬件上实现平衡的四级流水线设计,提高了运算速度．综合结果表明,采用中芯国际0．18μm工艺,数据吞吐量可达2．89Gb／s,优于目前发表的同类设计结果．     

双波长比值光谱差异度指数用于人体舌苔舌质分离

舌苔舌质信息定量描述作为中医舌诊的重要内容,直接影响到中医临床舌诊的准确性。基于生物医学光子学理论,利用高光谱技术,提出一种基于双波长比值光谱差异度指数进行人体舌质舌苔分离的光谱分析新方法。首先采集被测对象371.200～992.956 nm之间共343个波长的舌体高光谱信息,随机选取15位被测对象进行光谱特征分析。绘制15位被测对象舌质舌苔全波段光谱曲线并进行比较,通过观察发现,舌质舌苔反射光特征差异与血红蛋白在该波段的光学特征变化相吻合,在500～750 nm之间,水对光的吸收很少,而舌体表面布满血管,光的吸收主要受到血红蛋白的影响,基于舌质舌苔在573和700 nm两波段光谱吸收差异,计算双波长比值,提取舌质舌苔光谱特征差异度指数,根据个体差异,分别提取不同被测对象舌质舌苔光谱特征差异指标,进行舌质舌苔区域分离,实验结果发现,对同一被测对象舌体苔质提取光谱差异度指数SDI,舌苔舌质光谱差异度指数存在一定差异性,由于个体的不同,具有各自明显的舌质、舌体差异度指数分割线,实验结果表明,运用双波长比值光谱差异度指数的光学表达形式能够用于舌质舌苔分离,同时该方法也能够为进一步中医临床舌诊提供客观依据。