LS-based Methods Research Articles

Fast and almost unbiased weighted least squares fitting of circles

The algebraic fitting of circles was first proposed by Delogne (1972) and Kasa (1976). We extend the work by Delogne (1972) and Kasa (1976) and propose fast and almost unbiased weighted least squares to best fit circles. The simulations have shown that two non-iterative versions of the bias-corrected weighted LS method are fast and almost unbiased and perform much better than the naive weighted LS method (without applying any bias correction), the ordinary LS-based methods and the gradient-based weighted LS method in terms of both biases and mean squared errors, no matter whether fitting of circles is strongly or weakly constrained geometrically. Nevertheless, a weak geometrical constraint results in a poor fitting of circles. We accordingly propose the regularized variants of the bias-corrected weighted LS method to fit circles from data with a weak geometrical constraint. The simulations have also shown that the two non-iterative regularized variants fit circles satisfactorily well and consistently perform the best among all the regularization methods under study for ill-conditioned problems of fitting circles.

Estimation of the depth-domain seismic wavelet based on velocity substitution and a generalized seismic wavelet model

Depth-domain seismic wavelet estimation is the essential foundation for depth-imaged data inversion, which is increasingly used for hydrocarbon reservoir characterization in geophysical prospecting. The seismic wavelet in the depth domain stretches with increasing medium velocity and compresses with decreasing medium velocity. The commonly used convolutional model cannot be directly used to estimate depth-domain seismic wavelets due to velocity-dependent wavelet variations. We have developed a separate parameter estimation method for estimating depth-domain seismic wavelets from poststack depth-domain seismic and well-log data. Our method is based on the velocity substitution and depth-domain generalized seismic wavelet model defined by the fractional derivative and reference wavenumber. Velocity substitution allows wavelet estimation with the convolutional model in the constant-velocity depth domain. The depth-domain generalized seismic wavelet model allows for a simple workflow that estimates the depth-domain wavelet by estimating two wavelet model parameters. In addition, this simple workflow does not need to perform searches for the optimal regularization parameter and wavelet length, which are time-consuming in least-squares (LS)-based methods. The limited numerical search ranges of the two wavelet model parameters can easily be calculated using the constant phase and peak wavenumber of the depth-domain seismic data. Our method is verified using synthetic and real seismic data and further compared with LS-based methods. The results indicate that our method is effective and stable even for data with a low signal-to-noise ratio.

Spatial Fourier transform-based localized sound zone generation methods with loudspeaker arrays

This presentation provides spatial Fourier transform-based localized sound zone generation methods with multiple loudspeakers. First, these approaches are compared with conventional acoustic contrast and pressure matching approaches which are based on the least squares (LS) solution. Whereas these LS-based methods are unstable and some regularization schemes are required because the acoustic inverse problem is very ill-conditioned, the proposed spatial Fourier transform-based approaches can directly derive stable driving functions of loudspeakers without regularizations since the propagation and evanescent components of sound fields can be separated and only the propagation components are introduced to the driving functions. Then, spatial Fourier transform-based multiple sound zone generation methods with linear and circular loudspeaker arrays are introduced. In these approaches, the sound pressures on a line or a circle are modeled as rectangular or Hann windows, and the driving functions are analytically derived from the spatial Fourier transform. Additionally, localized sound zone generation approaches with linear, circular, and spherical loudspeaker arrays are introduced. In these approaches, the sound pressures produced by a loudspeaker are cancelled by the linear, circular, and spherical loudspeaker arrays. These driving functions are also derived from the spatial Fourier transform. Challenges and prospects of these approaches are finally described.

A Data-Driven Fuzzy Information Granulation Approach for Freight Volume Forecasting

The performance of the logistic system is one of the most important aspects in regional economy, and the freight volume is the biggest part of the logistic system. In this paper, an information granulation method is introduced to represent the freight volume in a fuzzy manner. After the characteristic features have been extracted from the raw time-series data and represented as information granules, the granules are modeled with the support vector machine (SVM). In consideration of both algorithm efficiency and prediction accuracy, an efficient version of SVM called least square (LS) SVM is employed and integrated with a parameter optimization algorithm, the particle swarm optimization. Simulation results on a real dataset illustrate the performance of the proposed method, and comparison studies are carried out with LS and partial LS-based methods.

A k-space operator-based least-squares staggered-grid finite-difference method for modeling scalar wave propagation

Two staggered-grid finite-difference (SGFD) schemes with fourth- and sixth-order accuracies in time have been developed recently based on new SGFD stencils. The SGFD coefficients of the two schemes are determined by a Taylor-series expansion (TE) approach, which is accurate only near a zero wavenumber. We have adopted the same SGFD stencils and determined the SGFD coefficients by minimizing the errors between the wavenumber responses of the SGFD operators and the first-order [Formula: see text] (wavenumber)-space operator in a least-squares (LS) sense. We solved the LS problems by performing a weighted pseudoinverse of nonsquare matrices to obtain the SGFD coefficients and to yield LS-based SGFD methods. We have developed an efficient LS implementation by using a small number of representative wavenumbers, which makes the computational time for estimating the coefficients negligible. Dispersion analysis and numerical examples demonstrate that our LS-based SGFD methods can preserve the original temporal accuracy and achieve better spatial accuracy than the existing TE-based SGFD methods. Extensive numerical tests proved that our LS-based methods do not damage the stability of the corresponding TE-based methods significantly.

Robust Multitask Multiview Tracking in Videos.

Various sparse-representation-based methods have been proposed to solve tracking problems, and most of them employ least squares (LSs) criteria to learn the sparse representation. In many tracking scenarios, traditional LS-based methods may not perform well owing to the presence of heavy-tailed noise. In this paper, we present a tracking approach using an approximate least absolute deviation (LAD)-based multitask multiview sparse learning method to enjoy robustness of LAD and take advantage of multiple types of visual features, such as intensity, color, and texture. The proposed method is integrated in a particle filter framework, where learning the sparse representation for each view of the single particle is regarded as an individual task. The underlying relationship between tasks across different views and different particles is jointly exploited in a unified robust multitask formulation based on LAD. In addition, to capture the frequently emerging outlier tasks, we decompose the representation matrix to two collaborative components that enable a more robust and accurate approximation. We show that the proposed formulation can be effectively approximated by Nesterov's smoothing method and efficiently solved using the accelerated proximal gradient method. The presented tracker is implemented using four types of features and is tested on numerous synthetic sequences and real-world video sequences, including the CVPR2013 tracking benchmark and ALOV++ data set. Both the qualitative and quantitative results demonstrate the superior performance of the proposed approach compared with several state-of-the-art trackers.

A new NIST primary standardization of 18F

A new primary standardization of 18F by NIST is reported. The standard is based on live-timed beta-gamma anticoincidence counting with confirmatory measurements by three other methods: (i) liquid scintillation (LS) counting using CIEMAT/NIST 3H efficiency tracing; (ii) triple-to-double coincidence ratio (TDCR) counting; and (iii) NaI integral counting and HPGe γ-ray spectrometry. The results are reported as calibration factors for NIST-maintained ionization chambers (including some “dose calibrators”). The LS-based methods reveal evidence for cocktail instability for one LS cocktail. Using an ionization chamber to link this work with previous NIST results, the new value differs from the previous reports by about 4%, but appears to be in good agreement with the key comparison reference value (KCRV) of 2005.

Robust suppression of nonstationary power-line interference in electrocardiogram signals

It is a challenge to suppress time-varying power-line interference (PLI) with various levels in electrocardiogram (ECG) signals. Most previous attempts of tracking and suppressing the nonstationary PLI signal are based on the least-squares (LS) algorithm. This makes these methods susceptible to QRS complex in suppressing a low-level PLI signal which is frequently coupled in battery-operated ECG equipment. To address the limitation of LS-based methods, this study presents a robust PLI suppression system based on a robust extension of the Kalman filter. In addition, we used an improved version of empirical mode decomposition to further attenuate the QRS complex. Experiments show that our system could effectively suppress the PLI while preserving meaningful ECG components at various interference levels.

Application of the least squares approach to fixed beamformer design with frequency-invariant constraints

An application of the least squares (LS) approach to the design of frequency-invariant beamformers is proposed, based on three different formulations of the problem. The first one is the traditional linearly constrained LS formulation with its solution given by the Lagrange multipliers method. The second and the third ones, which are formulated as an unconstrained LS problem and a constrained total LS problem, respectively, can be considered as extensions of the traditional total LS method and their solutions are obtained by finding the minimum generalised eigenvector of two matrices. Compared with the conventional LS-based methods, a frequency-invariance controlling element is incorporated into the proposed cost functions. Design examples including both broadside and off-broadside main beams are provided with a satisfactory frequency invariant property and sidelobe attenuation. The proposed approach is general and can be applied to different array structures.

Estimating Time-Varying Nonlinear Autoregressive Model Parameters by Minimizing Hypersurface Distance

A nonleast-squares (non-LS) based method is presented for modeling time-varying (TV) nonlinear systems. The proposed method combines basis function technique and minimization of hypersurface distance (MHD) to combat TV and nonlinear dynamics, respectively. The performance of TVMHD is compared to the LS and total LS methods using simulation examples as well as human heart rate data recorded during different body positions. With all data, TVMHD significantly outperforms the two other methods by a factor of one order of magnitude; the LS-based methods require double the number of parameters than TVMHD requires to obtain similar residual error values. The significance of TVMHD is that due to its accurate parameter estimates concomitant with a fewer number of parameters, we now have the possibility of pinpointing parameters that may be of physiological importance, where such application will be especially useful in discriminating diseased conditions. Furthermore, our algorithm allows discrimination of model terms, which are TV or time invariant, by examining those basis function coefficients that are designed to capture TV dynamics. However, it should be noted that the main disadvantage of TVMHD is that it requires significantly greater computational time than the LS-based methods.

基于最小绝对偏差估计的电视预测跟踪

To cope with the occlusion and intersection between targets and the environment, location prediction is employed in the visual tracking system. Target trace is fitted by sliding subsection polynomials based on least absolute deviation (LAD) estimation, and the future location of target is predicted with the fitted trace. Experiment results show that the proposed location prediction algorithm based on LAD estimation has significant robustness advantages over least square (LS) estimation, and it is more effective than LS-based methods in visual tracking.

On Estimation of Autoregressive Signals in the Presence of Noise

Estimation of autoregressive (AR) signals measured in white noise is considered. A well-known fact is that the measurement noise causes the least-squares (LS) estimate of the AR parameters to be biased. The kernel of an alternative method to be proposed is that, unlike the previous LS-based methods, a noniterative estimation scheme is established for the measurement white noise variance - the source of the bias. Numerical results demonstrate that the proposed method is much more cost effective in terms of computations and accuracy than the previous LS-based methods. The establishment of this noniterative unbiased estimation method also provides a mechanism for better understanding of the family of the LS-based methods

On the Formulation of Minimum-State Approximation as a Nonlinear Optimization Problem

The solution of the minimum-state (MS) approximation of the unsteady aerodynamic forces is brought in this work into the form of a nonlinear optimization problem. This new formulation takes as design variables all of the aerodynamic lag terms (known also as aerodynamic roots) as well as the two matrices that directly operate on these lag terms. This new formulation enables the explicit determination of the remaining matrices that form the MS approximation, and it does not require enforcing any equality constraints. Furthermore, it also permits the derivation of simple analytical expressions for the gradients of the least-square (LS)-type objective function. This combination of explicit expressions for both the gradients and some of the unknown matrices leads to a dramatic reduction in computational labor. It is also shown that by appropriately scaling the tabulated aerodynamic matrix a significantly accelerated rate of convergence is obtained during the process of optimization, whereas a general weighting scheme might considerably slow down this convergence. It is also shown that the preceding scaling of the tabulated aerodynamic matrix can also significantly reduce the computational labor required by current methods of solution that are based on iterative LS analysis. The new formulation presented in this work leads to better results (i.e., lower values for the objective function) than those obtained using current iterative LS-based methods that use preassumed values for the aerodynamic lag terms. At the same time, the computer CPU time required by these two methods of solution is of the same order, with only slightly higher CPU values needed for the new formulation. On the other hand, current methods based on iterative LS analysis that attempt to optimize the aerodynamic roots rather than use preassumed values need extensive added computational labor to the extent that makes them practically unattractive.