Noise estimation based on time–frequency correlation for speech enhancement

As a fundamental part of speech enhancement, noise estimation is particularly challenging in highly non-stationary noise environments. In this work, we propose an effective algorithm on the basis of the “Improved Minima Controlled Recursive Averaging (IMCRA)” with the objective to improve the performance of noise estimation. The main contributions of this work are: (i) in the algorithm, a rough decision about speech presence is proposed by calculating the autocorrelation and cross-channel correlation of the T–F (Time–Frequency) units; (ii) with this decision, we refine the smoothing parameters for the smoothing of noisy power spectrum and the recursive averaging in noise spectrum estimation as well as the weighting factor for the a priori SNR (Signal to Noise Ratio) estimation in the IMCRA; (iii) we improve the search of local minima during spectral bursts by adding a minimum search with a shorter window. Extensive experiments are carried out to evaluate the performance of our proposed algorithm. The experimental results illustrate that, compared with the IMCRA, the proposed approach significantly improves the accuracy of noise spectrum estimation and the quality of enhanced speech in the typical noise situations.     

The EPS method: A new method for constructing pseudospectral derivative operators

We develop a new type of derivative matrix for pseudospectral methods. The norm of these matrices grows at the optimal rate O(N²) for N-by-N matrices, in contrast to standard pseudospectral constructions that result in O(N⁴) growth of the norm. The smaller norm has a big advantage when using the derivative matrix for solving time dependent problems such as wave propagation. The construction is based on representing the derivative operator as an integral kernel, and does not rely on the interpolating polynomials. In particular, we construct second derivative matrices that incorporate Dirichlet or Neumann boundary conditions on an interval and on the disk, but the method can be used to construct a wide variety of commonly used operators for solving PDEs and integral equations. The construction can be used with any quadrature, including traditional Gauss–Legendre quadratures, but we have found that by using quadratures based on prolate spheroidal wave functions, we can achieve a near optimal sampling rate close to two points per wavelength, even for non-periodic problems. We provide numerical results for the new construction and demonstrate that the construction achieves similar or better accuracy than traditional pseudospectral derivative matrices, while resulting in a norm that is orders of magnitude smaller than the standard construction. To demonstrate the advantage of the new construction, we apply the method for solving the wave equation in constant and discontinuous media and for solving PDEs on the unit disk. We also present two compression algorithms for applying the derivative matrices in O(N log N) operations.     

Generator coordinate amplitude for scattering

In the generator coordinate method for scattering the proper boundary condition is accomplished by requiring the GC amplitude to satisfy an integral equation of the first kind. Attempts to solve this problem are first reviewed and then an improved approximation is proposed which is applicable to a wider class of scattering problems in addition to the Coulomb scattering.A better approximation is obtained in the asymptotic region, where the generator coordinate, i.e., the distance between two shell-model wells of the fragments, is larger than the touching distance of the colliding nuclei, by deriving partial differential equations of first order for the terms of an asymptotic series in $\text{1}\text{E}$, where E is the scattering energy.Extracting the information on the GC amplitude for small values of the generator parameter from the integral equation of the first kind is an ill-posed problem. It is shown that the method of statistical regularization offers a powerful and controllable procedure to uncover the GC amplitude. The unknown GC amplitude is treated as a random function with an a priori distribution of probability which is based on the assumption that the amplitude is bounded and that the errors in the input are random with zero expectation value. A useful procedure is found for fixing parameters of the a priori distribution. The solution for small values of the GC parameter is expressed in the form of a Dini series.The method is applied to the calculation of the GC amplitude for scattering of two α-particles at 15 MeV c.m. energy. The measure of the accuracy is the difference between the input wave function of relative motion and the result of folding of the GC amplitude with the kernel of the integral equation. The prescribed accuracy is reached with this method on a much larger interval than with any previously proposed method.     

A Generalized Estimate of the SLRBPolynomial Ripples for RF Pulse Generation

The nonlinearity of the parameter relations for the Shinnar–Le Roux RF pulse design algorithm has induced to performa classification based on the features of the slice profile dueto the RF pulse. In the present paper a generalization ofthe relation between the ripple amplitudes of the SLRBpolynomial and those of the slice profile is given. It allows generation of RF pulses with better slice profiles and slightly reduced energy, avoiding anya prioriclassification. The effect of our estimation has been shown by generating several pulses by generalized estimation ofBpolynomial ripples. In addition, their behavior has been compared to that of analogous pulses generated by means of the classification just mentioned.     

Single frame blind image deconvolution by non-negative sparse matrix factorization

Novel approach to single frame multichannel blind image deconvolution has been formulated recently as non-negative matrix factorization problem with sparseness constraints imposed on the unknown mixing vector that accounts for the case of non-sparse source image. Unlike most of the blind image deconvolution algorithms, the novel approach assumed no a priori knowledge about the blurring kernel and original image. Our contributions in this paper are: (i) we have formulated generalized non-negative matrix factorization approach to blind image deconvolution with sparseness constraints imposed on either unknown mixing vector or unknown source image; (ii) the criteria are established to distinguish whether unknown source image was sparse or not as well as to estimate appropriate sparseness constraint from degraded image itself, thus making the proposed approach completely unsupervised; (iii) an extensive experimental performance evaluation of the non-negative matrix factorization algorithm is presented on the images degraded by the blur caused by the photon sieve, out-of-focus blur with sparse and non-sparse images and blur caused by atmospheric turbulence. The algorithm is compared with the state-of-the-art single frame blind image deconvolution algorithms such as blind Richardson-Lucy algorithm and single frame multichannel independent component analysis based algorithm and non-blind image restoration algorithms such as multiplicative algebraic restoration technique and Van-Cittert algorithms. It has been experimentally demonstrated that proposed algorithm outperforms mentioned non-blind and blind image deconvolution methods.     

Direct solution of the equation of transfer using frequency- and angle-averaged photon escape probabilities,with application to a multistage,multilevel aluminum plasma

A formalism is developed which permits direct steady-state solution of the transfer equation using escape probabilities averaged over angle and frequency. A matrix of probability-based coupling coefficients, which are related to the kernel function K₁, is used to obtain the source function for a Doppler profile in plane-parallel geometry. Comparison is made with exact solutions, establishing the high accuracy of the technique. The method is extendable to different physical situations by simply modifying the coupling coefficients. As an example of a more realistic application of the formalism, we have solved for the ionization-excitation state of a planar aluminum plasma at 600 eV in collisional-radiative equilibrium. The results agree well with those obtained from the conventional multifrequency-multiangle formalism. Additionally, we have used the technique to gauge the effects of transport of lines connecting excited states with each other.     

Estimate of the J′J″ dependence of water vapor line broadening parameters

The dependence of water line broadening coefficients on the “good” quantum numbers − angular momentum and symmetry of the upper and lower levels − is analyzed for rotational quantum numbers up to J=50. Trends are investigated separately for P-, Q-, and R-branch transitions for the atmospherically important isotopologue of water. Results are presented which were obtained using two different methods: By averaging the broadening coefficients from HITRAN-2008 for small J values and also by averaging of data calculated using a semi-empirical method for higher J. The resulting air-broadening coefficients allow water vapor spectra with millions of weak lines to be calculated with an accuracy reasonable for many applications, for example estimation of sun radiation with low resolution. Sample results of calculations are presented.     

Fluctuation scaling and covariance matrix of constituents’ flows on a bipartite graph

We investigate an association between a power-law relationship of constituents’ flows (mean versus standard deviation) and their covariance matrix on a directed bipartite network. We propose a Poisson mixture model and a method to infer states of the constituents’ flows on such a bipartite network from empirical observation without a priori knowledge on the network structure. By using a proposed parameter estimation method with high frequency financial data we found that the scaling exponent and simultaneous cross-correlation matrix have a positive correspondence relationship. Consequently we conclude that the scaling exponent tends to be 1/2 in the case of desynchronous (specific dynamics is dominant), and to be 1 in the case of synchronous (common dynamics is dominant).     

Scattering theory of three-body systems

The Faddeev amplitude is expressed in the N/D form in terms of the real reciprocal matrix K. The S-matrix is written in the unitary form (1 + iπK)S = 1 ?iπK. The Breit-Wigner formula for the three-body system including the break-up channel is derived. In the present method, the three-body problem is reduced to solve the eigenvalue problem for the real symmetric kernel.     

基于两级压缩感知的脉冲星时延估计方法

为了快速获得高精度的脉冲星累积脉冲轮廓时延估计,提出了一种基于两级压缩感知的时延估计方法.压缩感知主要包括三个部分:字典、测量矩阵、恢复算法,其中字典尺寸是影响压缩感知估计精度的重要因素.针对压缩感知中字典的原子数增加虽能提高估计精度但又带来计算量大的问题,该方法采用粗估计与精估计两级字典相结合,先利用粗估计字典原子间隔大的特点进行累积脉冲轮廓全相位估计,得到预估时延值,再利用精估计字典的原子间隔小且个数少适合局部估计的特点对累积脉冲轮廓进行精确时延估计.理论分析与实验结果表明:两级字典数据量比传统字典小两个数量级,在相同的时延估计精度下,该方法比传统压缩感知方法计算量大幅度减少,是一种能保持高估计精度并有效降低计算量的脉冲星时延估计方法.     

Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations

This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions. Consequently, a full and strong coupling between both is hard to achieve due to this apparent incompatibility. This paper shows how to achieve this coupling in three steps.First, a new a priori error estimate is proved in a formal framework adapted to goal-oriented mesh adaptation for output functionals. This estimate is based on a careful analysis of the contributions of the implicit error and of the interpolation error. Second, the error estimate is applied to the set of steady compressible Euler equations which are solved by a stabilized Galerkin finite element discretization. A goal-oriented error estimation is derived. It involves the interpolation error of the Euler fluxes weighted by the gradient of the adjoint state associated with the observed functional. Third, rewritten in the continuous mesh framework, the previous estimate is minimized on the set of continuous meshes thanks to a calculus of variations. The optimal continuous mesh is then derived analytically. Thus, it can be used as a metric tensor field to drive the mesh adaptation. From a numerical point of view, this method is completely automatic, intrinsically anisotropic, and does not depend on any a priori choice of variables to perform the adaptation.3D examples of steady flows around supersonic and transsonic jets are presented to validate the current approach and to demonstrate its efficiency.     

On Eigenvalues of the Sum of Two Random Projections

We study the behavior of eigenvalues of matrix P _N +Q _N where P _N and Q _N are two N-by-N random orthogonal projections. We relate the joint eigenvalue distribution of this matrix to the Jacobi matrix ensemble and establish the universal behavior of eigenvalues for large N. The limiting local behavior of eigenvalues is governed by the sine kernel in the bulk and by either the Bessel or the Airy kernel at the edge depending on parameters. We also study an exceptional case when the local behavior of eigenvalues of P _N +Q _N is not universal in the usual sense.     

A lagrangian scheme for the solution of the optimal mass transfer problem

A lagrangian method to numerically solve the L² optimal mass transfer problem is presented. The initial and final density distributions are approximated by finite mass particles having a gaussian kernel. Mass conservation and the Hamilton–Jacobi equation for the potential are identically satisfied by constant mass transport along straight lines. The scheme is described in the context of existing methods to solve the problem and a set of numerical examples including applications to medical imagery are presented.     

Strength functions for fragmented doorway states

Coupling a strongly excited “doorway state” to weak “hallway states” distributes its strength into micro-resonances seen in differential cross sections taken with very good energy resolution. The distribution of strength is shown to be revealed by reduced widths of the K-matrix rather than by the imaginary part of poles of the S-matrix. Different strength functions (SF) constructed by averaging the K-matrix widths are then investigated to determine their dependences on energy and on parameters related to averages of microscopic matrix elements. A new sum rule on the integrated strength of these SF is derived and used to show that different averaging procedures actually distribute the strength differently. Finally, it is shown that the discontinuous summed strength defines spreading parameters for the doorway state only in strong coupling, where it approximates the indefinite integral of the continuous SF of MacDonald-Mekjian-Kerman-De Toledo Piza. A new method of “parametric continuation” is used to relate a discontinuous sliding box-average, or a finite sum, of discrete terms to a continuous function.     

Data-Based Optimal Bandwidth for Kernel Density Estimation of Statistical Samples

It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples, since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%~3% for sample size larger than 10⁴. This approach can also be generalized easily to cases of variable kernel estimations.     

Coarse-grained kinetic equations for quantum systems

The nonequilibrium density matrix method is employed to derive a master equation for the averaged state populations of an open quantum system subjected to an external high frequency stochastic field. It is shown that if the characteristic time τ_stoch of the stochastic process is much lower than the characteristic time τ_steady of the establishment of the system steady state populations, then on the time scale Δt ～ τ_steady, the evolution of the system populations can be described by the coarse-grained kinetic equations with the averaged transition rates. As an example, the exact averaging is carried out for the dichotomous Markov process of the kangaroo type.     

Half-metallic spin polarized electron states in the chimney-ladder higher manganese silicides MnSi1−x (x = 1.75 − 1.73) with silicon vacancies

We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation function is computed using a minimal phase recovering method. We illustrate our method on some examples and provide an empirical study of the estimation errors. Within this framework, we analyze high frequency financial price data modeled as 1D or 2D Hawkes processes. We find slowly decaying (power-law) kernel shapes suggesting a long memory nature of self-excitation phenomena at the microstructure level of price dynamics.     

Derivation of the radial distribution function from experimental Compton profiles

The analysis of experimental Compton profiles in position rather than momentum space provides a useful method of interpreting Compton data. A density matrix approach is employed to establish the relationship between the Compton profile J(p), and the Fourier transform of the momentum density B(r), and, for a homogeneous system, the radial distribution function g(r). An earlier Compton profile measurement on sodium provides the data for a demonstration of the long range charge correlations in a metal, in analogy with the Friedel oscillations in a screening charge.     

On the Distribution of the Wave Function for Systems in Thermal Equilibrium

For a quantum system, a density matrix ρ that is not pure can arise, via averaging, from a distribution μ of its wave function, a normalized vector belonging to its Hilbert space ?. While ρ itself does not determine a unique μ, additional facts, such as that the system has come to thermal equilibrium, might. It is thus not unreasonable to ask, which μ, if any, corresponds to a given thermodynamic ensemble? To answer this question we construct, for any given density matrix ρ, a natural measure on the unit sphere in ?, denoted GAP(ρ). We do this using a suitable projection of the Gaussian measure on ? with covariance ρ. We establish some nice properties of GAP(ρ) and show that this measure arises naturally when considering macroscopic systems. In particular, we argue that it is the most appropriate choice for systems in thermal equilibrium, described by the canonical ensemble density matrix ρ_β = (1/Z) exp (?β H). GAP(ρ) may also be relevant to quantum chaos and to the stochastic evolution of open quantum systems, where distributions on ? are often used.