Presence Of Gaussian Noise Research Articles

Robust stereo vision and calibration methodology for accurate three-dimensional digital image correlation measurements on submerged objects

The effect of optical refraction at an interface between optically dissimilar media is modelled in order to apply the principles of three-dimensional digital image correlation (DIC) to measure deformations on submerged objects accurately. Using an analytical formulation for refraction at an interface, a non-linear solution approach is developed to perform stereo calibration. The proposed method incorporates a simplified parametric representation for the orientation and position of an interface(s), accounting explicitly for the effects of refraction at all such interfaces in the path of each stereo camera. Separating the calibration process into two parts, a modified bundle adjustment process with an updated Levenburg—Marquardt (LM) non-linear optimization algorithm is employed to determine (a) intrinsic and extrinsic stereo camera parameters without interface refraction and (b) orientation and position of each planar interface. Detailed simulations demonstrate the efficiency, accuracy, and stability of the methodology when using multiple images of a grid pattern undergoing general rigid body motion, even in the presence of Gaussian noise in the sensor plane measurements, providing a robust framework for practical implementation of the methodology for submerged object measurements.

Robust super-resolution by minimizing a Gaussian-weighted L2 error norm

Super-resolution restoration is the problem of restoring a high-resolution scene from multiple degraded low-resolution images under motion. Due to imaging blur and noise, this problem is ill-posed. Additional constraints such as smoothness of the solution via regularization is often required to obtain a stable solution. While adding a regularization term to the cost function is a standard practice in image restoration, we propose a restoration algorithm that does not require this extra regularization term. The robustness of the algorithm is achieved by a Gaussian-weighted L2-norm in the data misfit term that does not response to intensity outliers. With the outliers suppressed, our solution behaves similarly to a maximum-likelihood solution in the presence of Gaussian noise. The effectiveness of our algorithm is demonstrated with super-resolution restoration of real infrared image sequences under severe aliasing and intensity outliers.

Tied Factor Analysis for Face Recognition across Large Pose Differences

Face recognition algorithms perform very unreliably when the pose of the probe face is different from the gallery face: typical feature vectors vary more with pose than with identity. We propose a generative model that creates a one-to-many mapping from an idealized "identity" space to the observed data space. In identity space, the representation for each individual does not vary with pose. We model the measured feature vector as being generated by a pose-contingent linear transformation of the identity variable in the presence of Gaussian noise. We term this model "tied" factor analysis. The choice of linear transformation (factors) depends on the pose, but the loadings are constant (tied) for a given individual. We use the EM algorithm to estimate the linear transformations and the noise parameters from training data. We propose a probabilistic distance metric which allows a full posterior over possible matches to be established. We introduce a novel feature extraction process and investigate recognition performance using the FERET, XM2VTS and PIE databases. Recognition performance compares favourably to contemporary approaches.

Point-Based Rigid-Body Registration Using an Unscented Kalman Filter

We present and validate a novel registration algorithm mapping two data sets, generated from a rigid object, in the presence of Gaussian noise. The proposed method is based on the Unscented Kalman Filter (UKF) algorithm that is generally employed for analyzing nonlinear systems corrupted by additive Gaussian noise. First, we employ our proposed registration algorithm to fit two randomly generated data sets in the presence of isotropic Gaussian noise, when the corresponding points between the two data sets are assumed to be known. Then, we extend the registration method to the case where the data (with known correspondences) is stimulated by anisotropic Gaussian noise. The new registration method not only reliably converges to the correct registration solution, but it also estimates the variance, as a confidence measure, for each of the estimated registration transformation parameters. Furthermore, we employ the proposed registration algorithm for rigid-body, point-based registration where corresponding points between two registering data sets are unknown. The algorithm is tested on point data sets which are garnered from a pelvic cadaver and a scaphoid bone phantom by means of computed tomography (CT) and tracked free-hand ultrasound imaging. The collected 3-D points in the ultrasound frame are registered to the 3-D meshes in the CT frame by using the proposed and the standard Iterative Closest Points (ICP) registration algorithms. Experimental results demonstrate that our proposed method significantly outperforms the ICP registration algorithm in the presence of additive Gaussian noise. It is also shown that the proposed registration algorithm is more robust than the ICP registration algorithm in terms of outliers in data sets and initial misalignment between the two data sets.

Probability density of the phase of a random RF pulse in the presence of Gaussian noise

In this paper, we show that the probability density function (pdf) of the phase of a random nonstationary radio frequency (RF) impulse signal perturbed by Gaussian noise does not depend on the multiple time derivatives of the signal amplitude and phase at a given time instance and is the Bennett's pdf. Employing this revealing, we derive an alternative form of the conditional pdf of the phase representing it with the von Mises/Tikhonov pdf conditional on the envelope, signal-to-noise ratio (SNR), and signal phase. We expend this new form to the Fourier series and investigate for the locked and unlocked reference phases. The error probability for the phase to exceed a threshold is also analyzed.

Improved super-exponential algorithm for blind equalization

Blind equalization is an effective way to suppress the inter-symbol interference (ISI), which is caused by multi-path fading communication channels. An improved super-exponential method (ISEM) is proposed here. The method, combining super-exponential method (SEM) and minimum description length (MDL), makes the equalization achieve good results even when the signal-to-noise ratio (SNR) is low. Compared with robust super-exponential method (RSEM) using fourth-order cumulants proposed by Kawamoto [M. Kawamoto, Robust super-exponential methods for blind equalization in the presence of Gaussian noise, IEEE Trans. Circuits Syst. II Express Briefs 52 (10) (2005) 651-655], the presented method has better robust performance but less computation.

Experimental demonstration of post-selection-based continuous-variable quantum key distribution in the presence of Gaussian noise

In realistic continuous-variable quantum key distribution protocols, an eavesdropper may exploit the additional Gaussian noise generated during transmission to mask her presence. We present a theoretical framework for a post-selection-based protocol which explicitly takes into account excess Gaussian noise. We derive a quantitative expression of the secret key rates based on the Levitin and Holevo bounds. We experimentally demonstrate that the post-selection-based scheme is still secure against both individual and collective Gaussian attacks in the presence of this excess noise.

Security of coherent-state quantum cryptography in the presence of Gaussian noise

We investigate the security against collective attacks of a continuous variable quantum key distribution scheme in the asymptotic key limit for a realistic setting. The quantum channel connecting the two honest parties is assumed to be lossy and imposes Gaussian noise on the observed quadrature distributions. Secret key rates are given for direct and reverse reconciliation schemes including post-selection in the collective attack scenario. The effect of a nonideal error correction and two-way communication in the classical post-processing step is also taken into account.

Baud-spaced constant modulus blind equalization via hybrid genetic algorithm and generalized pattern search optimization

The present paper deals with the formulation of the baud-spaced constant modulus blind equalization in the presence of Gaussian noise as an unconstrained optimization problem via the use of genetic algorithm and generalized pattern search (GPS) algorithm. Simulation results show that the proposed approach is more robust to the adopted initialization strategy and much more likely to outperform the classical constant modulus algorithm in terms of minimum-squared error, intersymbol interference and error vector magnitude quantities.

Non-parametric likelihood based channel estimator for Gaussian mixture noise

Extensive work to develop and optimise signal processing for signals that are corrupted by additive Gaussian noise has been done so far mainly because of the central limit theorem and the ease in analytic manipulations. It has been observed that the algorithms designed for Gaussian noise typically perform poor in presence of Gaussian mixture (non-Gaussian) noise. This paper discusses a likelihood based algorithm using kernel density estimates to improve channel estimation over a block in non-Gaussian noise environments. The likelihood pdf is assumed unknown and is estimated by using kernel density estimator at the receiver. A novel technique for channel estimation using a whitening filter for interference limited channels is also proposed in this paper. The performance of the proposed estimator is compared with the Cramér Rao lower bound for associated noise distribution. The simulations for impulsive noise and co-channel interference in presence of Gaussian noise, confirms that a better estimate can be obtained by using the proposed technique as compared to the traditional least-squares-based algorithms in highly non-Gaussian environments.

A comparison between the first absolute central moment and the gradient of Gaussian when detecting edges in presence of Gaussian noise

The gray-level absolute central moment of the first order provides ridges at gray-level discontinuities as well as a conventional gradient of Gaussian (GoG). A mass center b of the gray-level variability can also be associated to the first absolute central moment. When given a starting point p, vector b indicates the path which joins p to the nearest gray-level discontinuity as well as the gradient of the GoG magnitude. However, when the right configuration of the operator is chosen, vector b indicates a point which is closer to the discontinuity than p, regardless of the distance between p and the discontinuity. Therefore, when using vector b, gray-level discontinuities can be located with an iterative approach. In this paper, the edge detection properties of the first absolute central moment are compared with those of the GoG.

The influence of noise type and level upon stochastic resonance in human audition

The present study examined the extent to which noise type and fine differentiations in noise level produced improvements in auditory threshold via the mechanism of stochastic resonance. Participants’ thresholds for a sinusoidal signal (2.0 kHz) were estimated using a three interval forced choice task. These measures were obtained in quiet, in the presence of Gaussian noise, and in the presence of uniform (flat spectrum, zero-mean amplitude distribution) noise. The noises were presented at several levels from audible to inaudible (0.0 to −35.0 dB/Hz). The present results show that thresholds improved by a small, but significant, amount for noise levels just below subjects’ thresholds and that these improvements are not due solely to a simple summation of power between the signal and the noise. In addition, a subset of subjects showed larger and significant threshold increases at very low noise levels (−30.0 to −35.0 dB/Hz). The outcomes suggest that either Gaussian or uniform noise produces equivalent threshold improvements, SR may already be nearly optimized in persons with normal hearing, and that the maximum benefit possible from SR occurs over a narrow range of noise levels.

Error estimation in reconstruction of quadratic curves in 3D space

Many natural and man-made objects have planar and curvilinear surfaces. The images of such curves do not usually have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we describe a method for the reconstruction of various kinds of quadratic curves in 3D space as an intersection of two cones containing the respective projected digitized curve images in the presence of Gaussian noise. The advantage of this method is that it overcomes the correspondence problem that occurs in pairs of projections of the curve. Using nonlinear least-squares curve fitting, the parameters of a curve in 2D digitized image planes are determined. From this we reconstruct the 3D quadratic curve. Relevant mathematical formulations and analytical solutions for obtaining the equation of the reconstructed curve are given. Simulation studies have been conducted to observe the effect of noise on errors in the process of reconstruction. Results for various types of quadratic curves are presented using simulation studies. These are the main contributions of this work. The angle between the reconstructed and the original quadratic curves in 3D space has been used as the criterion for the measurement of the error. The results of this study are useful for the design of a stereo-based imaging system (such as the LBW decision in cricket, the path of a missile, robotic vision, path planning, etc.) and for the best reconstruction with minimum error.

Quality of Service of Broadband Fixed Wireless Access QPSK Channels Interfered by Adjacent Terrestrial Links

A physical model is presented concerning the quality of service (QoS) statistics of broadband fixed wireless access (BFWA) QPSK channels interfered by adjacent terrestrial links operating at the same frequency. The QoS is quantified in terms of the bit-error probability (BEP) of the link. BFWA networks of current interest are mainly operated above 10 GHz assuming line-of-sight (LoS) connection between the base station and the subscriber terminal. In these network configurations, rain attenuation is the dominant fading mechanism and its statistical behavior severely aggravates the nominal interference environment due to the spatial inhomogeneity of rain. The BEP of a coherent QPSK demodulator in the presence of Gaussian noise, cochannel interference and rain attenuation is determined and is related to the relevant performance masks recommended by ITU-R. Numerical results of the proposed model examine how the frequency of operation, the clear-sky interference levels, the length of the interfering path and the climatic conditions affect the QoS of BFWA channels. The spectral and spatial coexistence of BFWA networks and point-to-point links is investigated

Improving local Wiener filtering using matched filter

A new approach to local Wiener filtering in the presence of Gaussian noise is presented. The two-step denoising algorithm is formulated. In the first step, standard local Wiener filtering is applied. The output of the first step is used for the construction of the matched filter, which enables us to better estimate the signal energy. The signal energy estimate is then used for the construction of the improved local Wiener filter. The performance of this method, using the dual-tree complex wavelet transform, is evaluated. The results obtained are comparable with the best in the literature but at a significant smaller computational cost.

Robust super-exponential methods for blind equalization in the presence of Gaussian noise

This paper deals with the blind equalization problem of a single-input single-output infinite-impulse-response (SISO-IIR) system with additive Gaussian noise. To solve the problem, we propose a "super-exponential method" (SEM). The novel point of the proposed SEM is that, even when Gaussian noise is added to the output of the system, the blind equalization can be achieved with as little influence of Gaussian noise as possible; hence the proposed SEM is referred to as a "robust super-exponential method" (RSEM). Simulation results show the validity of the proposed RSEM.

Stochastic resonance in Gaussian and uniform noise

The improvement in threshold of a 2.0 kHz tone in the presence of low levels of uniform and Gaussian noise is compared to tonal threshold measured in quiet. Uniform noise was created using a rectangular amplitude distribution. The noises were low-pass filtered at 12.0 kHz and were presented continuously throughout a run at spectrum levels ranging from 0 to −30 dB/Hz. Pure-tone signals were 400 ms in duration including 10 ms raised cosine onset and offset ramps. Thresholds were obtained using a 3-interval, forced-choice procedure with correct answer feedback in conjunction with a two down, one up adaptive tracking paradigm that targets 70.7% correct on the psychometric function. Subjects were instructed to select the interval that was different from the others. Preliminary results for the Gaussian noise conditions are similar to earlier results [Zeng et al., Brain Res. 869, 251–255 (2000)]. Initial results for the uniform noise indicate that it produced equivalent or slightly lower thresholds than those measured in the presence of Gaussian noise.

The Distribution of Quantum Noise in the Presence of Gaussian Noise in the Fiber

In this paper we determined the distribution of quantum noise in the presence of variable light intensity. The distribution of quantum noise in the presence of variable light intensity is Poisson’s. The light intensity is variable because of different interferences. We considered the case when the light intensity has Gaussian pdf. Bibl. 4 (in English; summaries in Lithuanian, English and Russian).

Low complexity symbol detection method for multilevel 2-D optical storage based on a linear channel model

A symbol detection scheme based on the Viterbi algorithm that simultaneously processes subsets of 2-D data in the presence of Gaussian noise was recently proposed for binary 2-D optical storage (TwoDOS). In the case of multilevel TwoDOS, a straightforward full-fledged maximum likelihood symbol detector, or even the previous Viterbi-based algorithm, is not an ideal solution due to complexity restrictions. We propose a suboptimum low complexity symbol detector, which still performs within the accepted performance bound for optical storage. We describe the procedures involved in designing and developing a practical symbol detection scheme for multilevel TwoDOS by analyzing the signal values generated by a linear channel model in the presence of Gaussian noise. Our proposed detection scheme exploits the properties of the 2-D data format on the disk, and is flexible enough to accommodate performance and complexity restrictions for optical storage applications.

Von Mises/Tikhonov-based distributions for systems with differential phase measurement

The von Mises/Tikhonov probability density function (pdf) is examined to use as an approximation for the differential phase in presence of Gaussian noise in systems with differential phase measurement (DPM). It is shown that this approximation is the best fit for the phase difference between two vectors with equal signal-to-noise ratios (SNRs). The strategy is proposed to derive the approximate pdf for the case of infinite SNR in one of the vectors. Two approximating pdfs are derived for the differential phase diversity with different and equal SNRs. An application is given for the error probability in passive wireless remote SAW sensing with DPM.