The combined effect of spatial compounding and nonlinear filtering on the speckle reduction in ultrasound images

Recently, a spatial compounding ultrasound imaging method was presented that utilizes a conventional 64-element phased array transducer with two unfocused pistons, each placed at one of the sides of the phased array transducer. This method is augmented here by inclusion of nonlinear filtering of the compounded images. The combined effects of the specific spatial compounding and nonlinear filtering on speckle reduction in the generated ultrasound images are studied and evaluated in two stages: First, the image quality is studied when nonlinear filtering is used as part of the spatial compounding. The study is performed by simulations using the Field II program, by processing several B-mode images of a kidney. The second stage compares the results obtained by the simulations to those obtained by in vitro laboratory experiments. Five different compounding strategies and two nonlinear filters, Gaussian and anisotropic diffusion, are investigated and evaluated in terms of image quality parameters-contrast and signal-to-noise ratio. It is shown that the combination of "averaging+nonlinear Gaussian filtering" produces the greatest improvement of image quality. When compared to a conventional phased array imaging system, the spatial compounding method that includes the conventional 64-element phased array transducer with two unfocused pistons, and employs the "averaging+nonlinear Gaussian filtering" strategy, obtains improvement in SNR that has reached 334%. Thus, though this method necessitates a somewhat wider probe, it produces significantly improved images.     

A Numerical Approach to Copolymers at Selective Interfaces

We consider a model of a random copolymer at a selective interface which undergoes a localization/delocalization transition. In spite of the several rigorous results available for this model, the theoretical characterization of the phase transition has remained elusive and there is still no agreement about several important issues, for example the behavior of the polymer near the phase transition line. From a rigorous viewpoint non coinciding upper and lower bounds on the critical line are known. In this paper we combine numerical computations with rigorous arguments to get to a better understanding of the phase diagram. Our main results include:

Weak statistical convergence and weak filter convergence for unbounded sequences

For every weakly statistically convergent sequence (xn) with increasing norms in a Hilbert space we prove that . This estimate is sharp. We study analogous problem for some other types of weak filter convergence, in particular for the Erdös-Ulam filters, analytical P-filters and Fσ filters. We present also a refinement of the recent Aron-Garcia-Maestre result on weakly dense sequences that tend to infinity in norm.     

Noncentral elliptical configuration density

The noncentral configuration density, derived under an elliptical model, generalizes and corrects the Gaussian configuration and some Pearson results. Partition theory is then used to obtain explicit configuration densities associated with matrix variate symmetric Kotz type distributions (including the normal distribution), matrix variate Pearson type VII distributions (including t and Cauchy distributions), the matrix variate symmetric Bessel distribution (including the Laplace distribution) and the matrix variate symmetric Jensen-logistic distribution.     

Synergies among students’ thinking modes and representation types in linear algebra: employing statistical implicative analysis

In this work, students’ thinking modes and representation types in linear algebra are investigated through statistical implicative analysis techniques. Specifically, our research question considers the implicative relationships between students’ thinking modes and representation types of linear algebra. The participants were 74 undergraduate linear algebra students enrolled in the department of mathematics education of a government university located in western Turkey. The data was collected using six paper-and-pencil tasks, relating to a context of linear equations, matrix algebra, linear combination, span, linear independency–dependency and basis. A document analysis technique was used to analyze the data within a theoretical lens of thinking modes and representation types. To delineate similarity diagrams, hierarchical trees, and implicative models (which will be detailed in the paper), an R version of Cohesion Hierarchical Implicative Classification software was used. According to the results, students’ analytic structural thinking modes on linear combination and span and linear independency significantly imply the use of algebraic and abstract representations. The results also confirm that the notions of linear combination and span and linear dependency/independency are core elements for theoretical thinking and are needed for learning linear algebra.     

Statistical evaluation of uncertainty for rapid tests with discrete readings – examination of wastes and soils

 In the course of the colorimetric determination of analytes using a procedure with discrete readings the measurement uncertainly cannot be calculated in the normally practiced manner. The basic principle of the analytical method used is a stepwise and non-equidistant reading. Based on the fact that half a step can be estimated, a calculation of the measurement uncertainty for the 95% confidence level is possible; this is needed to allow a reliable decision of whether a critical value is exceeded or not. Received: 24 February 2000 / Accepted: 28 April 2000     

Hot and cold denaturation of proteins: Critical aspects

We argue that the first order hot and cold folding transitions of proteins observed at physiological chemical conditions ends in a critical point at a given temperature and chemical potential of the surrounding water. We investigate the properties of this critical point using a single-pathway scenario for the folding process. This pathway assumption determines the form of a Hamiltonian whose critical properties define a new universality class. Received 9 November 1998     

A Non-myopic Utility Function for Statistical Global Optimization Algorithms

The high cost of providing worst-case solutions to global optimization problems has motivated the development of average-case algorithms that rely on a statistical model of the objective function. The critical role of the statistical model is to guide the search for the optimum. The standard approach is to define a utility function u(x) that in a certain sense reflects the benefit of evaluating the function at x. A proper utility function needs to strike a balance between the immediate benefit of evaluating the function at x – a myopic consideration; and the overall effect of this choice on the performance of the algorithm – a global criterion. The utility functions currently used in this context are heuristically modified versions of some myopic utility functions. We propose using a new utility function that is provably a globally optimal utility function in a non-adaptive context (where the model of the function values remains unchanged). In the adaptive context, this utility function is not necessarily optimal, however, given its global nature, we expect that its use will lead to the improved performance of statistical global optimization algorithms. To illustrate the approach, and to test the above assertion, we apply this utility function to an existing adaptive multi-dimensional statistical global optimization algorithm and provide experimental comparisons with the original algorithm.     

关于灰色关联度中的几个问题的探讨

何文章、郭鹏．关于灰色关联度中的几个问题的探讨．本文通过理论分析及实例探讨了灰色关联度存在的主要缺陷,同时指出了不能用灰色关联度代替数理统计中的相关系数及多元统计分析方法。最后阐明了我们的观点及看法     

A new smoothing-regularization approach for a maximum-likelihood estimation problem

We consider the problem min _i=1 ^m (aⁱ,x–b_iloga ⁱ, z) subject tox 0 which occurs as a maximum-likelihood estimation problem in several areas, and particularly in positron emission tomography. After noticing that this problem is equivalent to mind(b, Ax) subject tox 0, whered is the Kullback-Leibler information divergence andA, b are the matrix and vector with rows and entriesa ⁱ,b _i, respectively, we suggest a regularized problem mind(b, Ax) + d(v, Sx), where is the regularization parameter,S is a smoothing matrix, andv is a fixed vector. We present a computationally attractive algorithm for the regularized problem, establish its convergence, and show that the regularized solutions, as goes to 0, converge to the solution of the original problem which minimizes a convex function related tod(v, Sx). We give convergence-rate results both for the regularized solutions and for their functional values.The research of A. N. Iusem was partially supported by CNPq Grant No. 301280/86-MA.