scholarly journals Fast Nonlinear Least Squares Optimization of Large‐Scale Semi‐Sparse Problems

2020 ◽  
Vol 39 (2) ◽  
pp. 247-259 ◽  
Author(s):  
M. Fratarcangeli ◽  
D. Bradley ◽  
A. Gruber ◽  
G. Zoss ◽  
T. Beeler
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Nonlinear Least Squares ◽  
Least Squares Optimization ◽  
Sparse Problems

scholarly journals Least Squares Optimization: From Theory to Practice

Robotics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 51 ◽  
Author(s):  
Giorgio Grisetti ◽  
Tiziano Guadagnino ◽  
Irvin Aloise ◽  
Mirco Colosi ◽  
Bartolomeo Della Corte ◽  
...  
Keyword(s):  
Computer Vision ◽  
Least Squares ◽  
Open Source ◽  
State Of The Art ◽  
Nonlinear Least Squares ◽  
Research Community ◽  
Specific Domain ◽  
Theory To Practice ◽  
Least Squares Optimization ◽  
Computer Vision Systems

Nowadays, Nonlinear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last few years, and this resulted in the development of several open-source solvers to approach constantly increasing classes of problems. In this work, we propose a unified methodology to design and develop efficient Least-Squares Optimization algorithms, focusing on the structures and patterns of each specific domain. Furthermore, we present a novel open-source optimization system that addresses problems transparently with a different structure and designed to be easy to extend. The system is written in modern C++ and runs efficiently on embedded systemsWe validated our approach by conducting comparative experiments on several problems using standard datasets. The results show that our system achieves state-of-the-art performances in all tested scenarios.

scholarly journals A Flow Perspective on Nonlinear Least-Squares Problems

2020 ◽  
Vol 48 (4) ◽  
pp. 987-1003
Author(s):  
Hans Georg Bock ◽  
Jürgen Gutekunst ◽  
Andreas Potschka ◽  
María Elena Suaréz Garcés
Keyword(s):  
Least Squares ◽  
Newton Method ◽  
Large Scale ◽  
Gradient Flow ◽  
Nonlinear Least Squares ◽  
Bundle Adjustment ◽  
Least Squares Problems ◽  
Flow Equations ◽  
Backward Euler ◽  
Forward Euler

AbstractJust as the damped Newton method for the numerical solution of nonlinear algebraic problems can be interpreted as a forward Euler timestepping on the Newton flow equations, the damped Gauß–Newton method for nonlinear least squares problems is equivalent to forward Euler timestepping on the corresponding Gauß–Newton flow equations. We highlight the advantages of the Gauß–Newton flow and the Gauß–Newton method from a statistical and a numerical perspective in comparison with the Newton method, steepest descent, and the Levenberg–Marquardt method, which are respectively equivalent to Newton flow forward Euler, gradient flow forward Euler, and gradient flow backward Euler. We finally show an unconditional descent property for a generalized Gauß–Newton flow, which is linked to Krylov–Gauß–Newton methods for large-scale nonlinear least squares problems. We provide numerical results for large-scale problems: An academic generalized Rosenbrock function and a real-world bundle adjustment problem from 3D reconstruction based on 2D images.

scholarly journals Near infrared nadir sounding of vertical column densities: methodology and application to SCIAMACHY

2011 ◽  
Vol 4 (3) ◽  
pp. 3685-3737
Author(s):  
S. Gimeno García ◽  
F. Schreier ◽  
G. Lichtenberg ◽  
S. Slijkhuis
Keyword(s):  
Least Squares ◽  
Near Infrared ◽  
Nonlinear Least Squares ◽  
Retrieval Algorithm ◽  
Atmospheric Gases ◽  
Vertical Column ◽  
Least Squares Fit ◽  
Least Squares Optimization ◽  
Shortwave Infrared ◽  
And Inversion

Abstract. Nadir observations with the shortwave infrared channels of SCIAMACHY onboard the ENVISAT satellite can be used to derive information on atmospheric gases such as CO, CH4, N2O, CO2, and H2O. For the operational level 1b–2 processing of SCIAMACHY data a new retrieval code BIRRA (Beer InfraRed Retrieval Algorithm) has been developed: BIRRA performs a nonlinear least squares fit of the measured radiance, where molecular concentration vertical profiles are scaled to fit the observed data. Here we present the forward modeling (radiative transfer) and inversion (least squares optimization) fundamentals of the code along with the further processing steps required to generate higher level products such as global distributions and time series. Moreover, various aspects of level 1 (observed spectra) and auxiliary input data relevant for successful retrievals are discussed. BIRRA is currently used for operational analysis of carbon monoxide vertical column densities from SCIAMACHY channel 8 observations, and is being prepared for methane retrievals using channel 6 spectra. A set of representative CO retrievals and first CH4 results are presented to demonstrate BIRRA's capabilities.

scholarly journals 2D shape deformation using nonlinear least squares optimization

2006 ◽  
Vol 22 (9-11) ◽  
pp. 653-660 ◽  
Author(s):  
Yanlin Weng ◽  
Weiwei Xu ◽  
Yanchen Wu ◽  
Kun Zhou ◽  
Baining Guo
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Shape Deformation ◽  
Least Squares Optimization

scholarly journals Forest Height Estimation Based on Constrained Gaussian Vertical Backscatter Model Using Multi-Baseline P-Band Pol-InSAR Data

2018 ◽  
Vol 11 (1) ◽  
pp. 42 ◽  
Author(s):  
Xiaofan Sun ◽  
Bingnan Wang ◽  
Maosheng Xiang ◽  
Shuai Jiang ◽  
Xikai Fu
Keyword(s):  
Least Squares ◽  
Incidence Angle ◽  
Nonlinear Least Squares ◽  
Estimation Accuracy ◽  
Height Estimation ◽  
Low Frequencies ◽  
Function Fitting ◽  
Forest Height ◽  
Vertical Heterogeneity ◽  
Least Squares Optimization

In the case of low frequencies (e.g., P-band) radar observations, the Gaussian Vertical Backscatter (GVB) model, a model that takes into account the vertical heterogeneity of the wave-canopy interactions, can describe the forest vertical backscatter profile (VBP) more accurately. However, the GVB model is highly complex, seriously reducing the inversion efficiency because of a number of variables. Given that concern, this paper proposes a constrained Gaussian Vertical Backscatter (CGVB) model to reduce the complexity of the GVB model by establishing a constraint relationship between forest height and the backscattering vertical fluctuation (BVF) of the GVB model. The CGVB model takes into account the influence of incidence angle on scattering mechanisms. The BVF of VBP described by the CGVB model is expressed with forest height and a polynomial function of incidence angle. In order to build the CGVB model, this paper proposes the supervised learning based on RANSAC (SLBR). The proposed SLBR method used forest height as a prior knowledge to determine the function of incidence angle in the CGVB model. In this process, the Random Sample Consensus (RANSAC) method is applied to perform function fitting. Before building the CGVB model, iterative weighted complex least squares (IWCLS) is employed to extract the required volume coherence. Based on the CGVB model, forest height estimation was obtained by nonlinear least squares optimization. E-SAR P-band polarimetric interferometric synthetic aperture radar (Pol-InSAR) data acquired during the BIOSAR 2008 campaign was used to test the performance of the proposed CGVB model. It can be observed that, compared with Random Volume over Ground (RVoG) model, the proposed CGVB model improves the estimation accuracy of the areas with incidence angle less than 0.8 rad and less than 0.6 rad by 28.57 % and 40.35 % , respectively.

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