Iterative Least-squares Method Research Articles

Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information

This article investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent factors; the other part models the effects of the observed covariates through a coefficient matrix which is composed of high-dimensional column vectors. We model the observational pattern of the responses through a logistic regression of the covariates, and allow its probability to go to zero as the sample size increases. We apply an iterative least squares (LS) estimation approach in our considered context. The iterative LS methods in general enjoy a low computational cost, but deriving the statistical properties of the resulting estimators is a challenging task. We show that our method only needs a few iterations, and the resulting entry-wise estimators of the low-rank matrix and the coefficient matrix are guaranteed to have asymptotic normal distributions. As a result, individual inference can be conducted for each entry of the unknown matrices. We also propose a simultaneous testing procedure with multiplier bootstrap for the high-dimensional coefficient matrix. This simultaneous inferential tool can help us further investigate the effects of covariates for the prediction of missing entries. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Design model-free adaptive PID controller based on lazy learning algorithm

Abstract The nonlinear system is difficult to achieve the desired effect by using traditional proportional integral derivative (PID) or linear controller. First, this study presents an improved lazy learning algorithm based on k-vector nearest neighbors, which not only considers the matching of input and output data, but also considers the consistency of the model. Based on the optimization index of an additional penalty function, the optimal solution of the lazy learning is obtained by the iterative least-square method. Second, based on the improved lazy learning, an adaptive PID control algorithm is proposed. Finally, the control effect under the condition of complete data and incomplete data is compared by simulation experiment.

Inversion of terrestrial water storage changes from GNSS vertical displacements using a priori constraint: A case study of the Yunnan Province, China

Global Navigation Satellite System (GNSS) is an effective means to monitor surface deformations associated with changes in terrestrial water storage (TWS). In this study, we introduced a priori constraint matrix and estimated the regularization parameter through an iterative least-squares method to infer the TWS changes using GNSS vertical displacements from December 2010 to February 2021 in the Yunnan Province (YNP), China. The GNSS-inferred TWS changes were validated through the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO) estimates, the Global Land Data Assimilation System (GLDAS) hydrological model, and the meteorological data (i.e., precipitation and Drought Severity Index (DSI)). The results demonstrate that the spatial resolution of TWS changes derived from 45 GNSS stations can reach 2°×2° in the YNP, and the a priori constraint is better than the traditional Laplacian matrix constraint for solving the discrete ill-conditioned problem of GNSS inversion. The GNSS-inferred TWS changes are consistent with the TWS changes derived from GRACE/GFO and GLDAS estimates in the spatio-temporal domains over the YNP, but the GNSS inversion results show stronger amplitudes. Furthermore, the ground-based GNSS observations are more sensitive to the TWS changes, and the correlation between precipitation and GNSS-inferred TWS changes is improved by about 11 % and 5 % compared to GRACE/GFO and GLDAS estimates in the YNP, respectively. The GNSS-inferred DSI can well reveal the two severe drought events in the YNP during the study period, which is consistent with the DSI derived from GRACE/GFO and GLDAS estimates, as well as the published self-calibrating Palmer Drought Severity Index (scPDSI) and the Standardized Precipitation-Evapotranspiration Index (SPEI). The GNSS observations can compensate the limitations of GRACE/GFO observations (e.g., bridging the data gap between GRACE and GFO missions), and help to better investigate the TWS changes in the YNP, which has significant potentials for regional water resource management and extreme climate changes monitoring.

Estimation of OH in urban plumes using TROPOMI-inferred NO2 ∕ CO

Abstract. A new method is presented for estimating urban hydroxyl radical (OH) concentrations using the downwind decay of the ratio of nitrogen dioxide over carbon monoxide column-mixing ratios (XNO2/XCO) retrieved from the Tropospheric Monitoring Instrument (TROPOMI). The method makes use of plumes simulated by the Weather Research and Forecast model (WRF-Chem) using passive-tracer transport, instead of the encoded chemistry, in combination with auxiliary input variables such as Copernicus Atmospheric Monitoring Service (CAMS) OH, Emission Database for Global Atmospheric Research v4.3.2 (EDGAR) NOx and CO emissions, and National Center for Environmental Protection (NCEP)-based meteorological data. NO2 and CO mixing ratios from the CAMS reanalysis are used as initial and lateral boundary conditions. WRF overestimates NO2 plumes close to the center of the city by 15 % to 30 % in summer and 40 % to 50 % in winter compared to TROPOMI observations over Riyadh. WRF-simulated CO plumes differ by 10 % with TROPOMI in both seasons. The differences between WRF and TROPOMI are used to optimize the OH concentration, NOx, CO emissions and their backgrounds using an iterative least-squares method. To estimate OH, WRF is optimized using (a) TROPOMI XNO2/XCO and (b) TROPOMI-derived XNO2 only. For summer, both the NO2/CO ratio optimization and the XNO2 optimization increase the prior OH from CAMS by 32 ± 5.3 % and 28.3 ± 3.9 %, respectively. EDGAR NOx and CO emissions over Riyadh are increased by 42.1 ± 8.4 % and 101 ± 21 %, respectively, in summer. In winter, the optimization method doubles the CO emissions while increasing OH by ∼ 52 ± 14 % and reducing NOx emissions by 15.5 ± 4.1 %. TROPOMI-derived OH concentrations and the pre-existing exponentially modified Gaussian function fit (EMG) method differ by 10 % in summer and winter, confirming that urban OH concentrations can be reliably estimated using the TROPOMI-observed NO2/CO ratio. Additionally, our method can be applied to a single TROPOMI overpass, allowing one to analyze day-to-day variability in OH, NOx and CO emission.

Fluid Identification Based on NMR Apparent Free Water Porosity Inversion: A Case Study of Paleozoic Tight Sandstone Gas Reservoirs in Western Ordos

Tight sandstone reservoirs are affected by various factors such as pore structure, formation water salinity, and siliceous cementation, which lead to the abnormal phenomenon of high-resistivity water layers and increase the difficulty in identifying gas and water layers by conventional logging. In this study, the pore types and pore size distribution characteristics of tight sandstone reservoirs were firstly determined by NMR and high-pressure mercury injection experiments, and then the iterative least-square method was used to automatically optimize the inversion method of pseudo-capillary pressure curve and search for the optimal conversion coefficient. Finally, the apparent free water porosity was inversed and the fluid identification standard was obtained and applied. The results showed that the reservoirs mainly developed intergranular pores, cutting solution pores, and intergranular pores. The pore throats were poorly sorted, and the displacement pressure was high. The median radius ranged from 0.01 to 0.48 μm, and the main peak range was from 0.02 to 0.06 μm. Pores were of mainly small-hole fine throat type. In the inversion results of the optimal conversion coefficient, the correlation coefficient between the aperture parameters and the results of high-pressure mercury injection experiments was greater than 0.93. According to the fluid property identification standard based on nuclear magnetic apparent free water porosity, the high-resistivity water layers were effectively identified and its coincidence rate with the final field test was 10.7% higher than that of the conventional method. This identification method can be used to identify complex fluids in tight sandstone reservoirs.

Ten-Minute Sea-Level Variations From Combined Multi-GNSS Multipath Reflectometry Based on a Weighted Iterative Least-Square Method

Accurate and high-frequency sea level monitoring is of great importance in ocean environments and global climatic studies, but traditional techniques have their respective limitations. In the last decades, the application of Global Navigation Satellite System Multipath Reflectometry (GNSS-MR) in sea level monitoring has developed rapidly. Recently, more available GNSS signals are expected to bring new opportunities to improve its performance and achieve high spatial-temporal resolution. In this paper, a new algorithm is developed to optimize the method of multi-GNSS multipath reflectometry and improve the precision and sampling rate for GNSS-MR sea level monitoring. In order to make full use of the short-term multipath oscillation information, a sliding window is used to collect the SNR sequences. A weighted iterative least-square method is introduced to combine the selected SNR observations of GPS, GLONASS, Galileo, and BDS systems, and retrieve sea level with 10-minute intervals at BRST station for one year. A novel index called Local Kurtosis (LK) is proposed, which can be used to evaluate the quality of the Lomb-Scargle periodogram (LSP) and design the weight matrix in the least-square combinatorial process. Compared to using individual signals, the optimized combination algorithm decreased the root mean square error (RMSE) by 78%, from 0.610 m to 0.134 m, and increased the correlation coefficient R² from 0.851 to 0.992. In addition, the tidal constituents monitored by multi-GNSS-MR and tide gauge are highly consistent, demonstrating that the multi-GNSS-MR can accurately retrieve daily and subdaily tidal constituents of periods longer than 10 min.

Automatic, Multiview, Coplanar Extraction for CityGML Building Model Texture Mapping

Most 3D CityGML building models in street-view maps (e.g., Google, Baidu) lack texture information, which is generally used to reconstruct real-scene 3D models by photogrammetric techniques, such as unmanned aerial vehicle (UAV) mapping. However, due to its simplified building model and inaccurate location information, the commonly used photogrammetric method using a single data source cannot satisfy the requirement of texture mapping for the CityGML building model. Furthermore, a single data source usually suffers from several problems, such as object occlusion. We proposed a novel approach to achieve CityGML building model texture mapping by multiview coplanar extraction from UAV remotely sensed or terrestrial images to alleviate these problems. We utilized a deep convolutional neural network to filter out object occlusion (e.g., pedestrians, vehicles, and trees) and obtain building-texture distribution. Point-line-based features are extracted to characterize multiview coplanar textures in 2D space under the constraint of a homography matrix, and geometric topology is subsequently conducted to optimize the boundary of textures by using a strategy combining Hough-transform and iterative least-squares methods. Experimental results show that the proposed approach enables texture mapping for building façades to use 2D terrestrial images without the requirement of exterior orientation information; that is, different from the photogrammetric method, a collinear equation is not an essential part to capture texture information. In addition, the proposed approach can significantly eliminate blurred and distorted textures of building models, so it is suitable for automatic and rapid texture updates.

An improved minimal error model for the robotic kinematic calibration based on the POE formula

SummaryThe conventional product of exponentials $\left(\rm POE\right)$ -based methods dissatisfy the parametric minimality for the kinematic calibration of serial robots due to overlooking the magnitude and pitch constraints. Thus, the minimal kinematic model is presented to solve this problem, which can be developed further. This paper puts forward an improved algorithm for the minimal parameter calibration. An actual kinematic model with the minimal parameters $\left(\rm MP\right)$ is constructed according to the geometric properties of actual joint twists in the auxiliary frames established on the basis of the nominal joint axes. Then, the initial pose error is defined in the tool coordinate frame, which is expressed as the exponential map of the twist, and all twist descriptions are unified, so as to give a unified kinematic model in mathematics. By differentiating the kinematic model, a minimal error model is derived in explicit form. Subsequently, we propose a novel parameter identification method, which identifies the orientation error and position error parameters separately by the iterative least-squares method and updates the MP uniformly. Finally, the simulations and experiments on the different serial robots are conducted to verify the correctness and effectiveness of the proposed algorithm. The simulation results show our calibration algorithm outperforms the existing ones in the accuracy aspect, and the experiment result shows that the absolute pose accuracy of the UR5 industrial robot is upgraded about 9 times under a statistics sense after the calibration.

Orbit error removal in InSAR/MTInSAR with a patch-based polynomial model

The orbit error caused by the inaccuracy of the orbit state vector can lead to fringes in differential interferograms, which can impede the estimation of deformation in differential SAR interferometry (DInSAR) applications. Usually, a set of polynomial coefficients for an entire SAR image is obtained for orbit error removal. However, the orbit error plane is influenced by overfitting in the case that the SAR satellites do not have a precise orbit. In this paper, a patch-based polynomial method is proposed to fit the orbit error plane. The new method divides an SAR image into several overlapping patches in the azimuth and range directions. Every patch obtains its own polynomial coefficients, and an iterative least-square method is used to mosaic the orbit plane. This method is tested and validated via a simulated dataset and then applied to ALOS1/2 PALSAR and Sentinel-1A datasets. The accuracy of deformation is evaluated by in situ GPS datasets. The results show that the patch-based method can fit the orbit phase plane more accurately than the traditional polynomial model with millimeter-level displacement improvement, especially in the margin areas of ALOS1/2 and for the wide-coverage Sentinel-1A datasets. Moreover, in the MTInSAR parameter calculations, the new method improves the accuracy of mean velocity calculations for ALOS1 time series, with a reduction of RMSE from 4.47 mm/yr to 3.17 mm/yr. Additionally, the new method reduces the spatial correlation of the residual topographic phase, with a mean value reduction from 0.32 m to 0.13 m.

An Iterative Least-Squares Method for Generated Jacobian Equations in Freeform Optical Design

The design of freeform optical surfaces is an inverse problem in illumination optics. Combining the laws of geometrical optics and energy conservation gives rise to a generalized Monge--Ampere equa...

A robust method for random noise suppression based on the Radon transform

Linear Radon transform, or slant-stack transform, can be used to obtain an optimally sparse representation of linear seismic events. The linear Radon transform uses a linear kernel function, and can stack the seismic data along several linear trajectories corresponding to specific slopes. The Radon transform can be formulated as a linear operator and the transform coefficients can be inverted via an iterative preconditioned least-squares method. The useful seismic signals are transformed as the sparse coefficients in the transform domain while the random noise are spreading across the transform domain or are not fitted via the Radon operator. It is advantageous to use a L2-norm data misfit to suppress the random noise but ineffective for high-amplitude erratic noise. Here, we propose a robust method to suppress both random and erratic noise based on the linear Radon transform. We iteratively transform the Huber-norm data-misfit regularization into a L2-norm regularization, which is convenient to solve using the preconditioned least-squares method. Both synthetic and field data examples are used to demonstrate the effectiveness of the proposed robust algorithm.

Limitations on the Positron Lifetime Spectra Decomposability Applying the Iterative Least-Square Re-Convolution Method Using the Instrumental Responses Obtained from 207Bi and 60Co

Limitations on the Positron Lifetime Spectra Decomposability Applying the Iterative Least-Square Re-Convolution Method Using the Instrumental Responses Obtained from ²⁰⁷Bi and ⁶⁰Co

Relativistic electron impact ionization cross sections of carbon ions and application to an optically thin plasma

Context.Ionization through electron impact is a fundamental process associated with the evolution of the ionic structure and emissivity of astrophysical plasmas. Over several decades substantial efforts have been made to measure and calculate the ionization cross sections of ionization through electron impact of different ions shell by shell, in particular, of carbon ions. Spectral emission codes use electron-impact ionization cross sections and/or rates taken from different experimental and theoretical sources. The theoretical cross sections are determined numerically and include a diversity of quantum mechanical methods. The electron-impact ionization database therefore is not uniform in the methods, which makes it hard to determine the reason for the deviations with regard to experimental data. In many cases only total ionization rates for Maxwell–Boltzmann plasmas are available, which makes calculating inner-shell ionization in collisional-radiative models using thermal and nonthermal electron distribution functions difficult. A solution of this problem is the capability of generating the cross sections with an analytical method using the minimum number of atomic parameters. In this way, uniformity in the database is guaranteed, and thus deviations from experiments are easily identified and traced to the root of the method.Aims.The modified relativistic binary encounter Bethe (MRBEB) method is such a simple analytical scheme based on one atomic parameter that allows determining electron-impact ionization cross sections. This work aims the determination of K- and L-shell cross sections of the carbon atom and ions using the MRBEB method and show their quality by: (i) comparing them with those obtained with the general ionization processes in the presence of electrons and radiation (GIPPER) code and the flexible atomic code (FAC), and (ii) determining their effects on the ionic structure and cooling of an optically thin plasma.Methods.The MRBEB method was used to calculate the inner-shells cross sections, while the plasma calculations were carried out with the collisional+photo ionization plasma emission software (CPIPES). The mathematical methods used in this work comprise a modified version of the double-exponential over a semi-finite interval method for numerical integrations, Gauss-elimination method with scaled partial pivoting for the solution of systems of linear equations, and an iterative least-squares method to determine the fits of ionization cross sections.Results.The three sets of cross sections show deviations among each other in different energy regions. The largest deviations occur near and in the peak maximum. Ion fractions and plasma emissivities of an optically thin plasma that evolves under collisional ionization equilibrium, derived using each set of cross sections, show deviations that decrease with increase in temperature and ionization degree. In spite of these differences, the calculations using the three sets of cross sections agree overall.Conclusions.A simple model like the MRBEB is capable of providing cross sections similar to those calculated with more sophisticated quantum mechanical methods in the GIPPER and FAC codes.

Reconstruction of CT Images Using Iterative Least-Squares Methods with Nonnegative Constraint

Reconstruction of CT Images Using Iterative Least-Squares Methods with Nonnegative Constraint

Automatic velocity analysis using high-resolution hyperbolic Radon transform

Velocity analysis is crucial in reflection seismic data processing and imaging. Velocity picking is widely used in the industry for building the initial velocity model. When the size of the seismic data becomes extremely large, we cannot afford the corresponding human endeavor that is required by the velocity picking. In such situations, an automatic velocity-picking algorithm is highly demanded. We have developed a novel automatic velocity-analysis algorithm that is based on the high-resolution hyperbolic Radon transform. We formulate the automatic velocity-analysis problem as a constrained optimization problem. To solve the optimization problem with a hard constraint on the sparsity and distribution of the velocity spectrum, we relax it to a more familiar L1-regularized optimization problem in two steps. We use the iterative preconditioned least-squares method to solve the L1-regularized problem, and then we apply the hard constraint of the target optimization during the iterative inversion. Using synthetic and field-data examples, we determine the successful performance of our algorithm.

Dynamic 3D shape measurement by iterative phase shifting algorithms and colored fringe patterns.

In this work, we propose a novel technique to retrieve 3D shape of dynamic objects by the simultaneous projection of a fringe pattern and a homogeneous white light pattern, both coded in an RGB image. The first one is used to retrieve the phase map by an iterative least-squares method. The second one is used to match object pixels in consecutive images, acquired at various object positions. The proposed method successfully accomplishes the requirement of projecting simultaneously two different patterns. One extracts the object's information while the other retrieves the phase map. Experimental results demonstrate the feasibility of the proposed scheme.

Multiparameter estimation using multi-echo spoiled gradient echo with variable flip angles and multicontrast compressed sensing.

To develop multiparameter mapping including T1 , R2*, and proton density fat fraction with a single breath-hold to evaluate liver disease and liver function. A 6-echo spoiled gradient-echo sequence with dual flip angles was used to acquire a 12-set MRI volume data set. To shorten the scan time, undersampling and multicontrast compressed-sensing reconstruction were used. The scan time was 18 seconds. R2* and proton density fat fraction mapping were achieved by using the iterative least-squares method. T1 mapping was estimated using driven equilibrium single-pulse observation of T1 . Quantitative values were validated by performing phantom and volunteer studies. Statistical analysis showed that the quantitative values measured using the proposed methods agreed with those measured using conventional methods. T1 values of water proton measured by the proposed method in phantom and volunteer studies were in good agreement with those by MRS. The results showed that accurate quantitative mapping of T1 , R2*, and proton density fat fraction with a single breath-hold was achieved using our approach.

Fast iterative equivalent-layer technique for gravity data processing: A method grounded on excess mass constraint

We have developed a new iterative scheme for processing gravity data using a fast equivalent-layer technique. This scheme estimates a 2D mass distribution on a fictitious layer located below the observation surface and with finite horizontal dimensions composed by a set of point masses, one directly beneath each gravity station. Our method starts from an initial mass distribution that is proportional to the observed gravity data. Iteratively, our approach updates the mass distribution by adding mass corrections that are proportional to the gravity residuals. At each iteration, the computation of the residual is accomplished by the forward modeling of the vertical component of the gravitational attraction produced by all point masses setting up the equivalent layer. Our method is grounded on the excess of mass and on the positive correlation between the observed gravity data and the masses on the equivalent layer. Mathematically, the algorithm is formulated as an iterative least-squares method that requires neither matrix multiplications nor the solution of linear systems, leading to the processing of large data sets. The time spent on the forward modeling accounts for much of the total computation time, but this modeling demands a small computational effort. We numerically prove the stability of our method by comparing our solution with the one obtained via the classic equivalent-layer technique with the zeroth-order Tikhonov regularization. After estimating the mass distribution, we obtain a desired processed data by multiplying the matrix of the Green’s functions associated with the desired processing by the estimated mass distribution. We have applied the proposed method to interpolate, calculate the horizontal components, and continue gravity data upward (or downward). Testing on field data from the Vinton salt dome, Louisiana, USA, confirms the potential of our approach in processing large gravity data set over on undulating surface.

Optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling

We investigate an optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling. An anti-lumped mass strategy is incorporated to minimize the numerical dispersion. The optimal finite-difference coefficients and the mass weighting coefficients are obtained by minimizing the misfit between the normalized phase velocities and the unity. An iterative damped least-squares method, the Levenberg–Marquardt algorithm, is utilized for the optimization. Dispersion analysis shows that the optimal fourth-order scheme presents less grid dispersion and anisotropy than the conventional fourth-order scheme with respect to different Poisson's ratios. Moreover, only 3.7 grid-points per minimum shear wavelength are required to keep the error of the group velocities below 1%. The memory cost is then greatly reduced due to a coarser sampling. A parallel iterative method named CARP-CG is used to solve the large ill-conditioned linear system for the frequency-domain modeling. Validations are conducted with respect to both the analytic viscoacoustic and viscoelastic solutions. Compared with the conventional fourth-order scheme, the optimal scheme generates wavefields having smaller error under the same discretization setups. Profiles of the wavefields are presented to confirm better agreement between the optimal results and the analytic solutions.

VTS 센서를 이용한 3D영상 분석에 기초한 파랑 정보 추출 알고리즘 성능 비교

해양사고가 빈번히 발생함에 따라 해상교통관제를 통해 항해의 안전성과 효율성을 개선하기 위한 해상 트래픽 모니터링 시스템을 구축할 필요성이 대두되고 있다. 이와 같은 목적을 위해, 최근에 X-대역 해양 레이더는 해수면 정보를 수집하는데 사용하고 있는데, 파랑 정보를 정확하게 측정하여 해상교통관제 영역 내에서 선박의 안전하고 효율적인 움직임을 제공하는 것이 요구된다. 본 논문에서는 세 가지의 다른 해류 속도를 산출하는 방법 즉, 최소자승법을 이용한 방법, 해류 속도를 반복 최소자승 갱신 방법, 가변적인 해류 속도의 정규화된 스칼라 곱을 극대화하여 해류 속도 추정치를 제공하는 방법 등에 대해 부이 데이터와 비교하고, 그런 후에 반복 갱신 방법을 수정하여 초기의 해류 속도를 개선하여 효과적으로 파랑 정보를 예측하도록 설계된다. 다수의 실험을 통하여 제안한 방법은 기존 방식에 비해 파랑 정보를 효과적으로 추출할 수 있음을 보인다. As marine accidents happen frequently, it is required to establish a marine traffic monitoring system, which is designed to improve the safety and efficiency of navigation in VTS (Vessel Traffic Service). For this aim, recently, X-band marine radar is used for extracting the sea surface information and, it is necessary to retrieve wave information correctly and provide for the safe and efficient movement of vessel traffic within the VTS area. In this paper, three different current estimation algorithms including the classical least-squares (LS) fitting, a modified iterative least-square fitting routine and a normalized scalar product of variable current velocities are compared with buoy data and then, the iterative least-square method is modified to estimate wave information by improving the initial current velocity. Through several simulations with radar signals, it is shown that the proposed method is effective in retrieving the wave information compared to the conventional methods.