Uncorrelated Gaussian Research Articles

Wiener discrete cosine transform-based image filtering

A classical problem of additive white (spatially uncorrelated) Gaussian noise suppression in grayscale images is considered. The main attention is paid to discrete cosine transform (DCT)-based denoising, in particular, to image processing in blocks of a limited size. The efficiency of DCT-based image filtering with hard thresholding is studied for different sizes of overlapped blocks. A multiscale approach that aggregates the outputs of DCT filters having different overlapped block sizes is proposed. Later, a two-stage denoising procedure that presumes the use of the multiscale DCT-based filtering with hard thresholding at the first stage and a multiscale Wiener DCT-based filtering at the second stage is proposed and tested. The efficiency of the proposed multiscale DCT-based filtering is compared to the state-of-the-art block-matching and three-dimensional filter. Next, the potentially reachable multiscale filtering efficiency in terms of output mean square error (MSE) is studied. The obtained results are of the same order as those obtained by Chatterjee's approach based on nonlocal patch processing. It is shown that the ideal Wiener DCT-based filter potential is usually higher when noise variance is high.

Conformational entropy of a polymer chain grafted to rough surfaces

A polymer molecule (represented by a statistical chain) end-grafted to a topologically rough surface was studied by static MC simulations. A modified self-avoiding walk on a cubic lattice was used to model the polymer in an athermal solution. Different statistical models of surface roughness were applied. Conformational entropies of chains attached to uncorrelated Gaussian, Brownian, and fractional Brownian surfaces were calculated. Results were compared with the predictions of a simple analytical model of a macromolecule end-grafted to a fractal surface. FigureVisualization of SAW generated by the (023) algorithm on a 3D cubic lattice Electronic supplementary materialThe online version of this article (doi:10.1007/s00894-012-1546-5) contains supplementary material, which is available to authorized users.

Scaling theory for percolative charge transport in molecular semiconductors: Correlated versus uncorrelated energetic disorder

We recently introduced a scaling theory for charge transport in molecular semiconductors with uncorrelated Gaussian energetic disorder, considering Miller-Abrahams as well as Marcus hopping and different lattice structures [Cottaar et al., Phys. Rev. Lett. 107, 136601 (2011)]. A compact expression was derived for the dependence of the charge-carrier mobility on temperature and carrier concentration. We show here that for Miller-Abrahams hopping the theory can also be applied to non-Gaussian energetic disorder, without parameter changes. Moreover, we show how it can be applied to correlated energetic disorder as obtained from randomly oriented molecular dipoles, which experiments suggest to be often more suitable. The same compact expression still describes the charge-carrier mobility, with new parameter values as determined from numerically exact results. The critical scaling exponent for correlated disorder is about twice as large as for uncorrelated disorder, which is caused by a different topology of the percolating network. The temperature dependence of the mobility for correlated disorder is significantly weaker than for uncorrelated disorder, while the carrier-concentration dependence is slightly weaker, due to small deviations of the density of states from a Gaussian. We indicate how comparison with experiments could distinguish between the different models.

On helical multiscale characterization of homogeneous turbulence

The helical properties of five prototypical homogeneous turbulent flows are investigated: statistically steady forced isotropic turbulence, decaying isotropic turbulence, decaying rotating turbulence, growing sheared turbulence, and growing rotating sheared turbulence with a rotation ratio f/S=+0.5. The five turbulent flows were originally studied using direct numerical simulations, and well-developed flow fields are chosen for this analysis. For comparison, a solenoidal uncorrelated Gaussian random field is included in the analysis as a sixth case. An orthogonal wavelet decomposition is used to study the scale-dependent properties of the cases. It is found that flows with growing turbulent kinetic energy and turbulent motion at large scales show a maximum in the relative kinetic helicity probability distribution functions (PDFs) at zero, corresponding to a trend to local two-dimensionalization of the flow with vorticity and velocity tending to be perpendicular. Flows with decaying turbulent kinetic energy and turbulent motion at small scales, however, show maxima of the relative kinetic helicity PDFs at plus and minus one, indicating a preference for helical motion with a trend to alignment or anti-alignment of vorticity and velocity. The PDFs of relative super-helicity always assume maxima at plus and minus one for all flows. The helical properties of statistically steady forced isotropic turbulence follow those of flows with decaying turbulent kinetic energy and a small asymmetry in the relative helicity PDFs is observed. Joint PDFs of relative kinetic helicity and relative super-helicity show that the quantities tend to have the same sign for all flows, including the random field, indicating that super-helicity dissipates kinetic helicity.

Reconstruction of Moving Target's HRRP Using Sparse Frequency-Stepped Chirp Signal

This paper introduces a novel reconstruction method of high-resolution range profile (HRRP) using sparse frequency-stepped chirp signal (FSCS). In the method, Compressed Sensing (CS) theory is utilized to reconstruct the moving target's HRRP. With this method even if the subpulses number of FSCS is incomplete, the HRRP can still be reconstructed successfully, and the final reconstructed ISAR image is clear enough for identification and classification of the target. Furthermore, the effect of noise is also analyzed by corrupting the data via an uncorrelated additive white Gaussian process.

Incorporating naturalistic correlation structure improves spectrogram reconstruction from neuronal activity in the songbird auditory midbrain.

Birdsong is comprised of rich spectral and temporal organization, which might be used for vocal perception. To quantify how this structure could be used, we have reconstructed birdsong spectrograms by combining the spike trains of zebra finch auditory midbrain neurons with information about the correlations present in song. We calculated maximum a posteriori estimates of song spectrograms using a generalized linear model of neuronal responses and a series of prior distributions, each carrying different amounts of statistical information about zebra finch song. We found that spike trains from a population of mesencephalicus lateral dorsalis (MLd) neurons combined with an uncorrelated Gaussian prior can estimate the amplitude envelope of song spectrograms. The same set of responses can be combined with Gaussian priors that have correlations matched to those found across multiple zebra finch songs to yield song spectrograms similar to those presented to the animal. The fidelity of spectrogram reconstructions from MLd responses relies more heavily on prior knowledge of spectral correlations than temporal correlations. However, the best reconstructions combine MLd responses with both spectral and temporal correlations.

The influence of CT image noise on proton range calculation in radiotherapy planning**Presented at the 51st Annual Meeting of the American Association of Physicists in Medicine, Anaheim, CA, July 26–30, 2009.

The purpose of this note is to evaluate the relationship between the stochastic errors in CT numbers and the standard deviation of the computed proton beam range in radiotherapy planning. The stochastic voxel-to-voxel variation in CT numbers called ‘noise,’ may be due to signal registration, processing and numerical image reconstruction technique. Noise in CT images may cause a deviation in the computed proton range from the physical proton range, even assuming that the error due to CT number-stopping power calibration is removed. To obtain the probability density function (PDF) of the computed proton range, we have used the continuing slowing down approximation (CSDA) and the uncorrelated white Gaussian noise along the proton path. The model of white noise was accepted because for the slice-based fan-beam CT scanner; the power-spectrum properties apply only to the axial (x, y) domain and the noise is uncorrelated in the z domain. However, the possible influence of the noise power spectrum on the standard deviation of the range should be investigated in the future. A random number generator was utilized for noise simulation and this procedure was iteratively repeated to obtain convergence of range PDF, which approached a Gaussian distribution. We showed that the standard deviation of the range, σ, increases linearly with the initial proton energy, computational grid size and standard deviation of the voxel values. The 95% confidence interval width of the range PDF, which is defined as 4σ, may reach 0.6 cm for the initial proton energy of 200 MeV, computational grid 0.25 cm and 5% standard deviation of CT voxel values. Our results show that the range uncertainty due to random errors in CT numbers may be significant and comparable to the uncertainties due to calibration of CT numbers.

Speech enhancement using linearly constrained adaptive constant directivity beam-formers

This paper aims to extend previous work on constant directivity beam-formers (CDBs), for the case of multiple desired speech sources, by designing a linearly constrained adaptive CDB (LCA-CDB) which preserves the beam-pattern in multiple look directions. Also, the proposed LCA-CDB, adaptively, minimizes the transient noise power in the output of the beam-former, and furthermore, produces some controlled nulls (controlled in both amplitude and angle) on the beam-pattern. This strengthens the system in removing permanent directional noises and producing a frequency-invariant beam-pattern with multiple main-lobes and controlled nulls in arbitrary frequency bands. Through simulating the system and the acoustical situations, the authors have tried to demonstrate the capability of the proposed method in enhancement of broadband and telephony speech in the presence of various noise sources (transient noise, permanent noise and uncorrelated white Gaussian noise). The simulation results obtained in this study confirm the efficiency of the proposed method in suppression of environmental noises.

A THEORETICAL ANALYSIS OF MULTISCALE ENTROPY UNDER THE INVERSE GAUSSIAN DISTRIBUTION

Multiscale entropy (MSE) discloses the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. Most of these research results are pure experimental search, till Costa et al. made the first attempt to the theoretical basis of MSE. However, the analysis only supports the Gaussian distribution [Phys. Rev. E71, 021906 (2005)]. In this paper, we present the theoretical basis of MSE under the inverse Gaussian distribution, which is a typical model for physiological, physical and financial data sets. The analysis is applicable to uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, providing a reliable foundation for potential applications of MSE to explore complex physical and physiological time series.

Functional changes induced by multiple plasticity rules in the hippocampal circuit: experiment and theory

We attempt to maximise mutual information in a neural network where the output signal is corrupted by noise in the transmission process to the next stage. We assume that the average power available for transmission is limited and that the transmission noise is uncorrelated equal-variance Gaussian noise. Using the Lagrange multiplier technique, we construct a utility function that should be maximised to achieve our optimum. This optimum will be achieved when the output signal components are also uncorrelated and of equal variance. For a linear network with lateral inhibitory connections, using an anti-Hebbian algorithm with modified self-inhibitory connections we guarantee to increase our utility function over time and converge to the required optimum, although not by steepest ascent. For a network with inhibitory interneurons, a combined Hebbian/anti-Hebbian algorithm will similarly increase the utility function over time to find the optimum. This network with interneurons suggests that negative feedback may be used in a perceptual system to optimise forward transmission of information.

An extended energy detector for non-Gaussian and non-independent noise

Energy detectors are optimum to detect uncorrelated Gaussian signals or generalized likelihood ratio tests to detect completely unknown signals; in both cases, background noise must be uncorrelated Gaussian. However, energy detectors degrade when background noise is non-independent and non-Gaussian. An extension is presented in this paper to deal with this situation. Independence is achieved by means of a matrix linear transformation derived from independent component analysis. Non-Gaussianity is avoided by applying a scalar non-linear function to every element of the linearly transformed observation vector. Practical procedures for estimating the linear and nonlinear transformations are given in the paper. A SNR enhancement factor has been defined for the weak signal case, which is indicative of the expected improvement of the proposed extension. Some simulations illustrate the achieved improvements.

Imaging Small PEC Spheres by a Linear $\delta$ Approach

The problem of localizing small inhomogeneities from the knowledge of their scattered field is dealt with. In particular, the case of small perfect electric conducting spheres is of concern, with the scattered field data collected under multistatic/multifrequency/single-view or multistatic/single-frequency/multiview far zone configurations. The multiple scattering between the spheres is neglected, and their locations are represented as the supports of the Dirac delta functions. This allows one to cast the problem as the inversion of a linear integral operator, with the delta functions being the unknowns of the problem. The inversion of this linear integral operator is achieved by means of the truncated singular value decomposition. The performance of the linear inversion algorithm against the model error (i.e., for situations where the multiple scattering is not negligible) is investigated by numerical simulations. Furthermore, the effect of noise is also analyzed by corrupting the data by an uncorrelated additive white Gaussian process.

Optimizing the performance of an MLP classifier for the automatic detection of epileptic spikes

This paper introduces different classification systems based on artificial neural networks for the automatic detection of epileptic spikes in electroencephalogram records. Different multilayer perceptron networks are constructed and trained with different algorithms. The inputs of the networks consist of either raw data or extracted features. To improve the generalization performance of the classifiers, “training with noise” method is used whereby new training data is constructed by adding uncorrelated Gaussian noise to real data. The performances of the constructed classifiers are examined and compared both with each other and with other similar systems found in literature based on sensitivity, specificity and selectivity measures.

STOCHASTIC DYNAMICS OF VISCOELASTIC SKEINS: CONDENSATION WAVES AND CONTINUUM LIMITS

Skeins (one-dimensional queues) of migrating birds show typical fluctuations in swarm length and frequent events of "condensation waves" starting at the leading bird and traveling backward within the moving skein, similar to queuing traffic waves in car files but more smooth.These dynamical phenomena can be fairly reproduced by stochastic ordinary differential equations for a "multi-particle" system including the individual tendency of birds to attain a preferred speed as well as mutual interaction "forces" between neighbors, induced by distance-dependent attraction or repulsion as well as adjustment of velocities. Such a one-dimensional system constitutes a so-called "stochastic viscoelastic skein."For the simple case of nearest neighbor interactions we define the density between individualsu = u(t, x) as a step function inversely proportional to the neighbor distance, and the velocity function v = v(t, x) as a standard piecewise linear interpolation between individual velocities. Then, in the limit of infinitely many birds in a skein of finite length, with mean neighbor distance δ converging to zero and after a suitable scaling, we obtain continuum mass and force balance equations that constitute generalized nonlinear compressible Navier–Stokes equations. The resulting density-dependent stress functions and viscosity coefficients are directly derived from the parameter functions in the original model.We investigate two different sources of additive noise in the force balance equations: (1) independent stochastic accelerations of each bird and (2) exogenous stochastic noise arising from pressure perturbations in the interspace between them. Proper scaling of these noise terms leads, under suitable modeling assumptions, to their maintenance in the continuum limit δ → 0, where they appear as (1) uncorrelated spatiotemporal Gaussian noise or, respectively, (2) certain spatially correlated stochastic integrals. In both cases some a priori estimates are given which support convergence to the resulting stochastic Navier–Stokes system.Natural conditions at the moving swarm boundaries (along characteristics of the hyperbolic system) appear as singularly perturbed zero-tension Neumann conditions for the velocity function v. Numerical solutions of this free boundary value problem are compared to multi-particle simulations of the original discrete system. By analyzing its linearization around the constant swarm state, we can characterize several properties of swarm dynamics. In particular, we compute approximating values for the averaged speed and length of typical condensation waves.

Effects of noise on periodic orbits of the logistic map

Abstract Noise can induce an inverse period-doubling transition and chaos. The effects of noise on each periodic orbit of three different period sequences are investigated for the logistic map. It is found that the dynamical behavior of each orbit, induced by an uncorrelated Gaussian white noise, is different in the mergence transition. For an orbit of the period-six sequence, the maximum of the probability density in the presence of noise is greater than that in the absence of noise. It is also found that, under the same intensity of noise, the effects of uncorrelated Gaussian white noise and exponentially correlated colored (Gaussian) noise on the period-four sequence are different.

The Influence of High Frequency Uncorrelated Noise on First-Break Arrival Times and Crosshole Traveltime Tomography

We investigate the influence of uncorrelated high frequency Gaussian noise on the accuracy and reliability of first-break arrival time picks. Using a reliable automatic picking algorithm based on the Akaike information criterion (AIC) and systematically noise contaminated synthetic data, allows us to develop a characteristic relation between the mis-pick (i.e., the error in the picked arrival time) and the signal-to-noise (S∕N) ratio for a specific waveform. For typical near-surface crosshole georadar survey setups, we further study the impact of such noise-related picking errors on tomographically reconstructed velocity images. Using synthetic and field data examples, results of tomographic inversions illustrate that significant velocity distortions can be introduced by noise-related mis-picking. In addition, we show that, under favorable conditions, it is possible to correct the noise-related picking errors prior to inversion.

Mathematical Force Concept for the One‐Way‐Coupling of Dynamic Fibers and Turbulent Flows

AbstractFor the modeling of turbulence effects on the dynamics of a long slender elastic fiber, a mathematical aerodynamic force concept is presented in this work. It yields a correlated random Gaussian force and respectively uncorrelated Gaussian white noise with flow‐dependent amplitude in the asymptotic limit on the macroscopic fiber scale. Numerical comparisons of the correlated and uncorrelated force effects on the fiber behavior show coinciding results. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effective temperatures in a simple model of non-equilibrium, non-Markovian dynamics

The concept of effective temperatures in nonequilibrium systems is studied within an exactly solvable model of non-Markovian diffusion. The system is coupled to two heat baths which are kept at different temperatures: one (‘fast’) bath associated with an uncorrelated Gaussian noise and a second ('slow') bath with an exponential memory kernel. Various definitions of effective temperatures proposed in the literature are evaluated and compared. The range of validity of these definitions is discussed. It is shown in particular, that the effective temperature defined from the fluctuation-dissipation relation mirrors the temperature of the slow bath in parameter regions corresponding to a separation of time scales. On the contrary, quasi-static and thermodynamic definitions of an effective temperature are found to display the temperature of the fast bath in most parameter regions.

Influence of head models on EEG simulations and inverse source localizations

BackgroundThe structure of the anatomical surfaces, e.g., CSF and gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the scalp potentials and the inverse source localizations. This was examined in detail with four different human head models.MethodsFour finite element head models constructed from segmented MR images of an adult male subject were used for this study. These models were: (1) Model 1: full model with eleven tissues that included detailed structure of the scalp, hard and soft skull bone, CSF, gray and white matter and other prominent tissues, (2) the Model 2 was derived from the Model 1 in which the conductivity of gray matter was set equal to the white matter, i.e., a ten tissue-type model, (3) the Model 3 was derived from the Model 1 in which the conductivities of gray matter and CSF were set equal to the white matter, i.e., a nine tissue-type model, (4) the Model 4 consisted of scalp, hard skull bone, CSF, gray and white matter, i.e., a five tissue-type model. How model complexity influences the EEG source localizations was also studied with the above four finite element models of the head. The lead fields and scalp potentials due to dipolar sources in the motor cortex were computed for all four models. The inverse source localizations were performed with an exhaustive search pattern in the motor cortex area. The inverse analysis was performed by adding uncorrelated Gaussian noise to the scalp potentials to achieve a signal to noise ratio (SNR) of -10 to 30 dB. The Model 1 was used as a reference model.ResultsThe reference model, as expected, performed the best. The Model 3, which did not have the CSF layer, performed the worst. The mean source localization errors (MLEs) of the Model 3 were larger than the Model 1 or 2. The scalp potentials were also most affected by the lack of CSF geometry in the Model 3. The MLEs for the Model 4 were also larger than the Model 1 and 2. The Model 4 and the Model 3 had similar MLEs in the SNR range of -10 dB to 0 dB. However, in the SNR range of 5 dB to 30 dB, the Model 4 has lower MLEs as compared with the Model 3.DiscussionThese results indicate that the complexity of head models strongly influences the scalp potentials and the inverse source localizations. A more complex head model performs better in inverse source localizations as compared to a model with lesser tissue surfaces. The CSF layer plays an important role in modifying the scalp potentials and also influences the inverse source localizations. In summary, for best results one needs to have highly heterogeneous models of the head for accurate simulations of scalp potentials and for inverse source localizations.

Performance of MIMO spatial multiplexing algorithms using indoor channel measurements and models

AbstractSeveral algorithms have recently been proposed for multiplexing multiple users in multiple input multiple output (MIMO) downlinks. The ability of a transmitter to accomplish this using spatial methods is generally dependent on whether the users' channels are correlated. Up to this point, most of the multiplexing algorithms have been tested on uncorrelated Gaussian channels, a best‐case scenario. In this paper, we examine the performance of multiplexing multiple users under more realistic channel conditions by using indoor channel measurements and a statistical model for test cases. We use a block zero‐forcing algorithm to test performance at various user separation distances, optimizing for both maximum throughput under a power constraint and minimum power under a rate constraint. The results show that for the measured indoor environment (rich scattering, non‐line‐of‐sight), a separation of five wavelengths is enough to achieve close to the maximum available performance for two users. Since many spatial multiplexing algorithms require channel state information (CSI) at the transmitter, we also examine the performance loss due to CSI error. The results show that a user can move up to one‐half wavelength before the original channel measurement becomes unusable. Copyright © 2004 John Wiley & Sons, Ltd.