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To suppress spectral drift in lengthy gamma spectrum measurements, a convenient and practical spectrum stabilization method with software-only adjustment is studied. The gamma energy spectra are recorded in consecutive small time intervals. The drifts in different time intervals relative to the first reference spectrum are estimated with a full spectrum nonlinear optimization technique, and the drifted spectra are corrected and accumulated to form a drift-free spectrum. This method needs neither hardware adjustment such as high voltage or electronics gain, nor peak location. Presented experimental results show that the stabilization accuracy can be significantly improved using this approach.

Purpose The purpose of this work was to develop and evaluate a T1-weighted dynamic contrast enhanced (DCE) MRI methodology where tracer-kinetic (TK) parameter maps are directly estimated from undersampled (k,t)-space data. Theory and Methods The proposed reconstruction involves solving a nonlinear least squares optimization problem that includes explicit use of a full forward model to convert parameter maps to (k,t)-space, utilizing the Patlak TK model. The proposed scheme is compared against an indirect method that creates intermediate images by parallel imaging and compressed sensing before to TK modeling. Thirteen fully sampled brain tumor DCE-MRI scans with 5-second temporal resolution are retrospectively undersampled at rates R = 20, 40, 60, 80, and 100 for each dynamic frame. TK maps are quantitatively compared based on root mean-squared-error (rMSE) and Bland-Altman analysis. The approach is also applied to four prospectively R = 30 undersampled whole-brain DCE-MRI data sets. Results In the retrospective study, the proposed method performed statistically better than indirect method at R ≥ 80 for all 13 cases. This approach provided restoration of TK parameter values with less errors in tumor regions of interest, an improvement compared to a state-of-the-art indirect method. Applied prospectively, the proposed method provided whole-brain, high-resolution TK maps with good image quality. Conclusion Model-based direct estimation of TK maps from k,t-space DCE-MRI data is feasible and is compatible up to 100-fold undersampling. Magn Reson Med 78:1566–1578, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

The mutual coupling, gain-phase error and sensor position error of the transmit and receive arrays would significantly degrade the performance of high-resolution direction of departure and direction of arrival estimation algorithms. By applying two well-calibrated instrumental sensors in both transmit and receive arrays, a novel angle estimation and self-calibration method, which considers the combined influences of the above three array errors, is proposed for bistatic MIMO radar. We show that the integrated array errors can be translated to angularly dependent gain-phase error. Then, a reduced dimensional method is used to estimate the angles and the angularly dependent gain-phase error coefficients. Based on the estimated angularly dependent gain-phase error coefficients, the nonlinear least squares optimization model for the three array errors are established and a quasi-Newton optimization method is applied to estimate the mutual coupling matrix, gain-phase error and sensors position errors of the transmit and receive arrays, respectively. Our simulation results corroborate our analysis.

The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers. Published version

The Cole impedance model is widely used in applications involving the electrical impedance of biological tissues. Typically requiring post-processing to determine its four parameters from electrical impedance measurements. Here, a nonlinear least squares optimization routine is applied to extract the Cole impedance parameters from collected magnitude responses (not requiring direct impedance measurements). The aim is to quantify the impact of the measured frequency range, number of collected datapoints, and level of noise in the magnitude-only measurements on the accuracy of the extracted parameters. Further investigating the impact the optimization settings have on the accuracy and time required to extract the parameters. The aim is to understand these factors' effects towards the implementation of embedded systems utilizing this method to extract the impedance parameters.

A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138---1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples.

A better understanding of individual subject ozone (O(3)) exposure response kinetics will provide insight into how to improve models used in the risk assessment of ambient ozone exposure.To develop a simple two compartment exposure-response model that describes individual subject decrements in forced expiratory volume in one second (FEV(1)) induced by the acute inhalation of O(3) lasting up to 8 h.FEV(1) measurements of 220 subjects who participated in 14 previously completed studies were fit to the model using both particle swarm and nonlinear least squares optimization techniques to identify three subject-specific coefficients producing minimum "global" and local errors, respectively. Observed and predicted decrements in FEV(1) of the 220 subjects were used for validation of the model. Further validation was provided by comparing the observed O(3)-induced FEV(1) decrements in an additional eight studies with predicted values obtained using model coefficients estimated from the 220 subjects used in cross validation.Overall the individual subject measured and modeled FEV(1) decrements were highly correlated (mean R(2) of 0.69 ± 0.24). In addition, it was shown that a matrix of individual subject model coefficients can be used to predict the mean and variance of group decrements in FEV(1).This modeling approach provides insight into individual subject O(3) exposure response kinetics and provides a potential starting point for improving the risk assessment of environmental O(3) exposure.

This study presents an analysis of a cerebral autoregulation (CA) model developed by Ursino and Lodi Ursino and Lodi (1997). We have used this model to analyze non-invasive measurements of cerebral blood flow velocity (CBFV) and arterial blood pressure obtained during postural change from sitting to standing for a healthy young subject. This paper includes a sensitivity analysis, ranking model parameters from the most to the least sensitive, and an analysis (using a methodology called subset selection) that allows identification of correlations among model parameters. Finally, we estimated patient specific parameters using the Levenberg-Marquardt optimization method minimizing the least square errors between computed and measured values of CBFV.

The output limits of the power system stabilizer (PSS) can improve the system damping performance immediately following a large disturbance. Due to non-smooth nonlinearities from the saturation limits, these values cannot be determined by the conventional tuning methods based on linear analysis. Only ad hoc tuning procedures have been used. A nonlinear least squares method, which is the Gauss-Newton optimization algorithm, is used in this paper. The gradient required in the Gauss-Newton method can be computed by applying trajectory sensitivities from the hybrid system model with the differential-algebraic-impulsive-switched (DAIS) structure. The optimal output limits of the PSS tuned by the proposed method are evaluated by time-domain simulation in a multi-machine power system (MMPS).

The variation of the friction in the roll bite is of great importance in cold strip rolling. The main interest of the paper is to model the friction coefficient in the roll bite during cold rolling. The deformation resistance of the rolled products and friction coefficient in the roll bite were determined simultaneously by minimizing the error of the measured and calculated rolling forces based on nonlinear least squares optimization algorithm. The neural network was introduced to further improve the accuracy of friction coefficient calculation in cold strip rolling. The results already obtained shows that friction decreases with roll wear, and the lower the rolling speed, the higher is the friction.

This paper presents a new approach to shaping of the frequency response of the sensitivity function. In this approach, a desired frequency response is assumed to be specified at a finite number of frequency points. A sensitivity shaping problem is formulated as an approximation problem to the desired frequency response with a function in a class of sensitivity functions with a degree bound. The sensitivity shaping problem is reduced to a finite-dimensional constrained nonlinear least-squares optimization problem. To solve the optimization problem numerically, standard algorithms for an unconstrained version of nonlinear least-squares problems are modified to incorporate the constraint. Numerical examples illustrate how these design parameters are tuned in an intuitive manner, as well as how the design proceeds in actual control problems.

The Levenberg Marquardt (LM) algorithm is a popular nonlinear least squares optimization technique for solving data matching problems. In this method, the damping parameter plays a vital role in determining the convergence of the system. This damping parameter is calculated arbitrarily in the classical LM, causing it to converge prematurely when used for solving real world engineering problems. This paper focuses on changes made to the classical LM algorithm to enhance its performance. This is achieved by adaptive damping, wherein the damping parameter is varied depending on the convergence of the objective function. To eliminate the need for a good initial guess, the idea of using an evolutionary algorithm in conjunction with the LM algorithm is also explored.

In this paper a novel method is presented for the identification of sparse dynamical interaction networks, such as gene regulatory networks. This method uses mixed L2/L1 minimization: nonlinear least squares optimization to achieve an optimal fit between the model in state space form and the data, and L1-minimization of the parameter vector to find the sparsest such model possible. In this approach, in contrast to previous research, the dynamical aspects of the model are taken into account, which gives rise to a nonlinear estimation problem. The setup allows for the identification of structured or partially sparse models, so that available prior knowledge on interactions can be incorporated. To investigate the potential for applications, the algorithm is tested on artificial gene regulatory networks.

This paper investigates the use of a wireless sensor network (WSN) for estimating the location of an event source that releases a certain signal or substance in the environment which is then propagated over a large area. The concentration of the substance at the source location is assumed unknown. The sensor nodes are able to measure the substance concentration at their own locations but the measurements are noisy. Based on these concentration readings we use nonlinear Least Squares (LS) optimization to estimate the event source position. Such a network can be of tremendous help for environmental monitoring or for emergency personnel responding to a catastrophic event. Our simulation results indicate that the LS method performs significantly better that the Closest Point Approach (CPA) where the source location is assumed to be the sensor node with the highest measurement. Furthermore, our results indicate that in the presence of a "draft" that pushes the substance in certain direction, a threshold is necessary for the LS method to yield accurate results. In addition, our results show that the use of unconstrained optimization or the existing knowledge of the wind direction can further improve the performance of the location estimate.

This paper proposes the use of a sensor network for estimating the location of a source that releases certain substance in the environment which is then propagated over a large area. More specifically, we use nonlinear least squares optimization to estimate the source position based on the concentration readings at the sensor nodes. Such a network can be of tremendous help to emergency personnel trying to protect people from terrorist attacks or responding to an accident. Our results indicate that in high uncertainty environments it pays off to use a large number of sensors in the estimation whereas in low uncertainty scenarios a few sensors achieve satisfactory results. In addition, our results point out the importance of choosing the appropriate parameters for the least squares optimization especially the start position for our algorithm. We compare our results to the Closest Point Approach (CPA) where the source location is assumed to be the sensor node with the highest measurement. ©2005 IEEE.

Much work has already been realized concerning the association of surfaces to points digitized with a Coordinate Measuring Machine (CMM). The developed procedures are usually based on the minimization of the distance between the measured points and the geometric element. They depend on the criterion used for the optimization. The function to minimize is always non-linear. To reduce the computing time, it is therefore transformed usually into linear variational equations, which are solved by an iterative process. Such algorithms require however to define initial parameters close to the final solution. The method presented here is based on a nonlinear least squares optimization. It does not require any coordinate transformation and is not sensitive to the selection of initial intrinsic parameters. It applies to all the classical surfaces, i.e. lines, planes, circles, cylinders, cones and spheres. In accordance with quality standards, the uncertainties of the estimated parameters are also defined. These values are derived from the residue between the measured points and the optimized associated surface.

This work deals with closed-loop calibration methods where the robot endpoint is constrained to lie on a plane. Previously published calibration approaches are shown to have certain weaknesses. A new solution is given using DH and Hayati notations and standard nonlinear least squares optimization. The procedure is extended via the implicit loop method, which takes input noise into account. Pose selection is guided by the noise amplification index. Simulation and experimental results are presented for a PUMA 560 industrial manipulator and are compared to those obtained from an open-loop calibration procedure.

The authors describe the use of a nonlinear least squares optimization technique for adaptively determining the equivalent source locations when the method of fundamental solution is used for 2D eddy current problems. The main advantage of the method is that guesswork in locating the sources is eliminated. Two examples of applying the method are given. One is the case of two circular conductors (one magnetic and the other nonmagnetic). The second is the case of a single conductor having a rectangular cross section. In both cases, the conductors carry an impressed current. Results are compared with those obtained without the use of nonlinear least squares optimization. It is shown that in both cases the source points can easily go across the boundaries during the optimization procedure. >

External coincidence counting was used for simultaneous estimation, in the 2-fluoro-2-deoxy-D-glucose (2-FDG) model, of the lumped and apparent rate constants (i.e., for a white/gray matter mixture). Eleven normal cats were studied. During a programmed 2-[18F]FDG infusion that kept a constant arterial plasma concentration of 2-[18F]FDG [Cp*(t)] for 45 minutes, the time course of cerebral tissue activity [Ci*(t)] was monitored by external coincidence counting. The apparent rate constants were estimated from Ci*(t) and Cp*(t) by a nonlinear least squares optimization method. The lumped constant (LC) estimate was obtained by fitting the ratio of extraction fractions of glucose and 2-[18F] FDG by use of a nonweighted, nonlinear least squares fitting method. The estimated apparent rate constants, k1*, k2*, k3*, and the LC were 0.074 ± 0.005 min-1, 0.129 ± 0.007 min-1, 0.021 ± 0.001 min-1, and 0.395 ± 0.016, respectively (mean ± SEM). The focal cerebral metabolic rate for glucose detected in the brain was 28.7 ± 1.5 μmol/100 gm/min (mean ± SEM). The influence of arterial plasma glucose (CP), the LC, and the metabolic index [MI = k1*k3*/(k2* + k3*)] on the stability of the cerebral glucose utilization rate was examined. Negative correlations between CP and LC, and CP and MI were observed. However, there was a positive correlation between the LC and the MI. The method applied in this study should be very useful in the detection of changes in the kinetics of 2-[18F]FDG under pathophysiological conditions in animals. Because of the short half-life of this isotope, repeated measurements are possible.

This paper proposes a novel and iterative way to conduct model order reduction (MOR) of linear equivalent circuit models (ECMs) without the use of a state-space representation as a surrogate model. The result is an ECM with a reduced total number of circuit elements but same system behavior. The proposed method is as follows: first, the original ECM is decomposed into smaller subcircuits after which a variance-based global sensitivity analysis by means of polynomial chaos expansion is conducted in order to extract the Sobol indices which measure the relative impact of the circuit elements. The least influential ones are then removed by either shorting them or replacing them by an electric open. The frequency responses of the resulting reduced circuits are then fitted against the original frequency response through nonlinear least squares optimization and by subsequently updating the element values. As opposed to the traditional MOR techniques from systems theory, the proposed approach operates on the ECM themselves directly. Thus, it not only offers additional physical insight into the system at any iteration step but also inherently leads to reduced-order models that are at once stable, causal, and passive. This makes the approach especially useful for practical electromagnetic compatibility problems and analysis. In the following, this novel approach is first described in detail and then applied to different test cases. Finally, a discussion of its limitations will be given.