Modified Gauss-Newton Algorithm Research Articles

A Krylov subspace type method for Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications in medical imaging for the detection and location of bodily tumors since it is an affordable and non-invasive method, which aims to recover the internal conductivity of a body using voltage measurements resulting from applying low frequency current at electrodes placed at its surface. Mathematically, the reconstruction of the internal conductivity is a severely ill-posed inverse problem and yields a poor quality image reconstruction. To remedy this difficulty, at least in part, we regularize and solve the nonlinear minimization problem by the aid of a Krylov subspace-type method for the linear sub problem during each iteration. In EIT, a tumor or general anomaly can be modeled as a piecewise constant perturbation of a smooth background, hence, we solve the regularized problem on a subspace of relatively small dimension by the Flexible Golub-Kahan process that provides solutions that have sparse representation. For comparison, we use a well-known modified Gauss–Newton algorithm as a benchmark. Using simulations, we demonstrate the effectiveness of the proposed method. The obtained reconstructions indicate that the Krylov subspace method is better adapted to solve the ill-posed EIT problem and results in higher resolution images and faster convergence compared to reconstructions using the modified Gauss–Newton algorithm.

Modified Gauss–Newton Algorithm for Evaluation of Full Lightning Impulse Voltage Parameters

Modified Gauss–Newton Algorithm for Evaluation of Full Lightning Impulse Voltage Parameters

A modified Gauss-Newton algorithm for fast microwave imaging using near-field probes

A modified Gauss-Newton algorithm for fast microwave imaging using near-field probes

A quadratic polynomial signal model and fuzzy adaptive filter for frequency and parameter estimation of nonstationary power signals

Accurate estimation of amplitude, phase and frequency of a sinusoid in the presence of harmonics/inter harmonics and noise plays an important role in a wide variety of power system applications, like protection, control and state monitoring. With this objective, the paper presents a novel hybrid approach for the accurate estimation of dynamic power system frequency, phasor and in addition to suppressing the effect of harmonics/interharmonics and noise in the voltage and current signals. The algorithm assumes that the current during a fault occurring on a power system consists of a decaying dc component, and time variant fundamental and harmonic phasors. For accurate estimation of fundamental frequency, phasor, decaying dc and ac components in the fault current or voltage signal, the algorithm uses a quadratic polynomial signal model and a fuzzy adaptive ADALINE filter with a modified Gauss–Newton algorithm. Extensive study has been carried out to demonstrate the performance analysis and fast convergence characteristic of the proposed algorithm. The proposed method can also be implemented for accurate estimation of dynamic variations in the amplitude and phase angles of the harmonics and inter harmonics mixed with high noise conditions.

Subgrade Dynamic Backcalculation Based on PFWD

In order to evaluate the bearing capacity and the compaction performance of subgrade in a reasonable way, according to the time history results of pressure and displacement tested with the PFWD (Portable Falling Weight Deflectometer), the extraction methods of time history data were put forward to use for the backcalculation. Combined with the analytic solutions of dynamic response of vertical displacement on the half-space surface under the impact loading of semi-sine wave in the circular rigid vertical distribution for the dynamic half-space theory, the mathematical models of subgrade dynamic backcalculation were established based on the least square criterion, then the corresponding backcalculation flow and method were proposed in accordance with the modified Gauss-Newton algorithm. Firstly the pressure time history was fitted as a semi-sine wave to obtain the two backcalculation parameters of impact load, i.e. the angular velocity and the nonresponsive period. Secondly the displacement time history was fitted to obtain the two subgrade dynamic parameters, i.e. the dynamic modulus and the dynamic density. Lastly, through comparing the dynamic backcalculation to the static backcalculation from the tested data, the results show that the dynamic modulus is substantially equal to the static modulus, and there are the well correlations between the dynamic density and the dry density and the moisture content measured with the sand replacement method. Therefore, the PFWD can simultaneously test the design index (modulus) and the construction index (compactness) for the subgrade to achieve the both unified evaluation.

COMPARISON AND ANALYSIS OF NONLINEAR LEAST SQUARES METHODS FOR VISION BASED NAVIGATION (VBN) ALGORITHMS

Abstract. A robust scale and rotation invariant image matching algorithm is vital for the Visual Based Navigation (VBN) of aerial vehicles, where matches between an existing geo-referenced database images and the real-time captured images are used to georeference (i.e. six transformation parameters - three rotation and three translation) the real-time captured image from the UAV through the collinearity equations. The georeferencing information is then used in aiding the INS integration Kalman filter as Coordinate UPdaTe (CUPT). It is critical for the collinearity equations to use the proper optimization algorithm to ensure accurate and fast convergence for georeferencing parameters with the minimum required conjugate points necessary for convergence. Fast convergence to a global minimum will require non-linear approach to overcome the high degree of non-linearity that will exist in case of having large oblique images (i.e. large rotation angles).The main objective of this paper is investigating the estimation of the georeferencing parameters necessary for VBN of aerial vehicles in case of having large values of the rotational angles, which will lead to non-linearity of the estimation model. In this case, traditional least squares approaches will fail to estimate the georeferencing parameters, because of the expected non-linearity of the mathematical model. Five different nonlinear least squares methods are presented for estimating the transformation parameters. Four gradient based nonlinear least squares methods (Trust region, Trust region dogleg algorithm, Levenberg-Marquardt, and Quasi-Newton line search method) and one non-gradient method (Nelder-Mead simplex direct search) is employed for the six transformation parameters estimation process. The research was done on simulated data and the results showed that the Nelder-Mead method has failed because of its dependency on the objective function without any derivative information. Although, the tested gradient methods succeeded in converging to the relative optimal solution of the georeferencing parameters. In trust region methods, the number of iterations was more than Levenberg-Marquardt because of the necessity for evaluating the local minimum to ensure if it is the global one or not in each iteration step. As for the Levenberg-Marquardt method, which is considered as a modified Gauss-Newton algorithm employing the trust region approach where a scalar is introduced to assess the choice of the magnitude and the direction of the descent. This scalar determines whether the Gauss-Newton method direction or the steepest descent method direction will be used as an adaptive approach for both linear and non-linear mathematical models and it successfully converged and achieved the relative optimum solution. These five methods results are compared explicitly to the linear traditional least-squares approach, with detailed statistical analysis of the results, with emphasis on the UAV (VBN) applications.

Independent estimation ofT*2for water and fat for improved accuracy of fat quantification

Noninvasive biomarkers of intracellular accumulation of fat within the liver (hepatic steatosis) are urgently needed for detection and quantitative grading of nonalcoholic fatty liver disease, the most common cause of chronic liver disease in the United States. Accurate quantification of fat with MRI is challenging due the presence of several confounding factors, including T*(2) decay. The specific purpose of this work is to quantify the impact of T*(2) decay and develop a multiexponential T*(2) correction method for improved accuracy of fat quantification, relaxing assumptions made by previous T*(2) correction methods. A modified Gauss-Newton algorithm is used to estimate the T*(2) for water and fat independently. Improved quantification of fat is demonstrated, with independent estimation of T*(2) for water and fat using phantom experiments. The tradeoffs in algorithm stability and accuracy between multiexponential and single exponential techniques are discussed.

Identification of dynamic systems using Piecewise-Affine basis function models

Piecewise-Affine (PWA) Basis Function AutoRegressive eXogenous (BPWARX) models are proposed in this paper for nonlinear black-box identification. A BPWARX model is a weighted sum of PWA Basis (BPWA) functions, which are the minimum or maximum of n + 1 affine functions in n dimensions. Since the BPWA functions have a universal representation capability for continuous PWA functions, the BPWARX models provide better accuracy than the Hinging Hyperplane ARX (HHARX) models with the same number of parameters, and the same order of computational complexity, when using a modified Gauss–Newton algorithm to build the models from input–output data.

Improved Parametric Image Generation Using Spatial-Temporal Analysis of Dynamic PET Studies

The value of parametric images that represent both spatial distribution and quantification of the physiological parameters of tracer kinetics has long been recognized. However, the inherent high noise level of pixel kinetics of dynamic PET makes it unsuitable to generate parametric images of the microparameters of tracer kinetic model by conventional weighted nonlinear least squares (WNLS) fitting. Based on the concept that both spatial and temporal information should be integrated to improve parametric image quality, a nonlinear ridge regression with spatial constraint (NLRRSC) parametric imaging algorithm was proposed in this study. For NLRRSC, a term that penalizes local spatial variation of parameters was added to the cost function of WNLS fitting. The initial estimates and spatial constraint were estimated by component representation model (CRM) with cluster analysis. A hierarchical cluster with average linkage method was used to extract components. The ridge parameter was determined by linear ridge regression theory at each iteration, and a modified Gauss–Newton algorithm was used for minimizing the cost function. Results from a computer simulation showed that the percent mean square error of estimates obtained by NLRRSC can be decreased by 60–80% compared to that of WNLS. The parametric images estimated by NLRRSC are significantly better than the ones generated by WNLS. A highly correlated linear relationship was found between the ROI values calculated from the microparametric images generated by NLRRSC and estimates from ROI kinetic fitting. NLRRSC provided a reliable estimate of glucose metabolite uptake rate with a comparable image quality compared to Patlak analysis. In conclusion, NLRRSC is a reliable and robust parametric imaging algorithm for dynamic PET studies.

Recovery of atomic oxygen density and temperature of the thermosphere by numerical inversion of simulated infrared radiance data with gaussian noise

It is demonstrated that the recovery of oxygen atom density and temperature atmospheric profiles can be obtained from numerical inversion of simulated limb-look radiance from the two atomic oxygen far infra-red fine-structure transitions at 63 μ m ( 3 P 1 → 3 P 2) and 128 μ m ( 3 P 0 → 3 P 1) . The inversion of simulated radiance data with reasonable estimates of noise is possible if both the integrated radiance and line-center radiance are available for both transitions. In order for the recovery of the atmospheric parameters to be successful down to regions of high oxygen atom density (100 km), it is necessary to smooth the noisy radiance data prior to application of a modified Gauss-Newton algorithm. Best results were obtained when a combination of cubic spline and optimal filtering smoothing techniques were used.

A mathematical model for the impact of energy input in land preparation on yield of rice

The present investigation deals with the nature of variation of yield corresponding to different levels of energy input in land preparation in the case of transplanted rice. The data recorded for the response of rice yield are compatible with the exponential law of diminishing returns. Use is made of the modified Gauss-Newton algorithm to compute the least square estimates of the parameters associated with the response curve. An attempt is also made to construct 95% confidence intervals for the parameters involved. Achievement of moderate reduction in commercial energy expenditure in land preparation with a very small reduction in rice yield, is suggested by the asymptotic nature of the response curve.

Mössbauer spectrum curve fitting with a personal computer

A method to perform Mössbauer spectrum curve fitting with a personal computer is presented. A modified Gauss-Newton algorithm for the least squares determination of nonlinear parameters is used in order to write computer codes that perform satisfactorily within the small memory sizes of personal computers. Mössbauer spectrum curve fitting with an IBM AT personal computer takes about 20 minutes of computing time to fit a pure Fe sextet spectrum and about 2 hours to fit a relatively complicated spectrum. The quality of the curve fitting with the personal computer is identical to that fitted with a mainframe computer.

Linear recursive adaptive equalization utilizing a modified Gauss - Newton algorithm

A new tap update algorithm is developed for linear recursive adaptive equalizers. This algorithm is an extension of the Modified Gauss-Newton algorithm, a least-squares method, which has been successfully used to compute the coefficients for recursive digital filters [13], [19]. The new algorithm is an on-line technique but the taps are updated periodically rather than on a symbol-by-symbol basis. This block update procedure has the advantage of providing time to perform the calculations required to update the taps. The Modified Gauss-Newton algorithm is compared with recursive equalizers that attempt to minimize the mean-squared error by means of stochastic gradient update algorithms. It is shown, via Monte-Carlo computer simulation, that by utilizing more information than simply the gradient, improved performance is obtained. In particular, the algorithm is much less sensitive to the eigenvalue ratio corresponding to the distortion. Convergence speed and error performance of the new algorithm are favorably compared with the Least-Squares Adaptive Lattice Equalizer.

Estimation of kinetic parameters of a grinding-liberation model

A method of parameter estimation is outlined for a two-component grinding-liberation model. The large number of model variables is reduced by using functional forms. The parameters for the functional forms are estimated using a modified Gauss-Newton algorithm. The technique is applied to both synthetic and real experimental data. Parameters estimated from wet grinding batch tests of Illinois No. 6 coal were used to predict mill output for a larger pilot-plant mill. The predictions were found to match the actual mill output within the limits of experimental error.

Estimation of covariance structure models with parameters subject to functional restraints

This paper demonstrates the feasibility of using the penalty function method to estimate parameters that are subject to a set of functional constraints in covariance structure analysis. Both types of inequality and equality constraints are studied. The approaches of maximum likelihood and generalized least squares estimation are considered. A modified Scoring algorithm and a modified Gauss-Newton algorithm are implemented to produce the appropriate constrained estimates. The methodology is illustrated by its applications to Heywood cases in confirmatory factor analysis, quasi-Weiner simplex model, and multitrait-multimethod matrix analysis.