Design Method of a Regularization Parameter for L1-Norm Minimization Problem Based on Statistics

2015 ◽  
Vol 135 (11) ◽  
pp. 1419-1426
Author(s):  
Yasuaki Kaneda ◽  
Yasuharu Irizuki
Keyword(s):  
Minimization Problem ◽  
Regularization Parameter ◽  
Design Method ◽  
Norm Minimization

A new piecewise quadratic approximation approach for L0 norm minimization problem

2018 ◽  
Vol 62 (1) ◽  
pp. 185-204 ◽  
Author(s):  
Qian Li ◽  
Yanqin Bai ◽  
Changjun Yu ◽  
Ya-xiang Yuan
Keyword(s):  
Minimization Problem ◽  
Quadratic Approximation ◽  
Approximation Approach ◽  
Norm Minimization

A-optimal design method to determine the regularization parameter of coseismic slip distribution inversion

2020 ◽  
Vol 221 (1) ◽  
pp. 440-450
Author(s):  
Leyang Wang ◽  
Wangwang Gu
Keyword(s):  
Optimal Design ◽  
Regularization Parameter ◽  
Design Method ◽  
Slip Distribution ◽  
Coseismic Slip ◽  
Seismic Slip ◽  
Regularization Parameters ◽  
Curve Method ◽  
Optimal Design Method

ABSTRACT The key to the inversion of a coseismic slip distribution is to determine the regularization parameters. In view of the determination of regularization parameters in seismic slip distribution inversion, the A-optimal design method is proposed in this paper. The L-curve method and A-optimal design method are used to design simulation experiments, and the inversion results show that the A-optimal design method is superior to the L-curve method in determining the regularization parameters. These two methods are also used to determine the regularization parameters of the L'Aquila and Lushan earthquake slip distribution inversions, and the results are consistent with those of other research conducted at home and abroad. Compared with the L-curve method, the A-optimal design method has the advantages of a high accuracy that does not rely on the data fitting accuracy.

scholarly journals Inverse potential problems in divergence form for measures in the plane

2021 ◽  
Author(s):  
Laurent Baratchart ◽  
Douglas Hardin ◽  
Cristobal Villalobos-Guillén
Keyword(s):  
Vector Fields ◽  
Regularization Parameter ◽  
Tangent Vector ◽  
Thin Plates ◽  
Total Variation Norm ◽  
Infinite Dimensional ◽  
Jordan Curves ◽  
Norm Minimization ◽  
Potential Problems ◽  
Noise Limit

We study inverse potential problems with source term the divergence of some unknown (R 3 -valued) measure supported in a plane; e.g., inverse magnetization problems for thin plates. We investigate methods for recovering a magnetization μ by penalizing the measure-theoretic total variation norm kμk T V , and appealing to the decomposition of divergence-free measures in the plane as superpositions of unit tangent vector fields on rectifiable Jordan curves. In particular, we prove for magnetizations supported in a plane that T V -regularization schemes always have a unique minimizer, even in the presence of noise. It is further shown that T V -norm minimization (among magnetizations generating the same field) uniquely recovers planar magnetizations in the following two cases: (i) when the magnetization is carried by a collection of sufficiently separated line segments and a set that is purely 1-unrectifiable; (ii) when a superset of the support is tree- like. We note that such magnetizations can be recovered via T V -regularization schemes in the zero noise limit by taking the regularization parameter to zero. This suggests definitions of sparsity in the present infinite dimensional context, that generate results akin to compressed sensing.

Structural Parameters Optimization of Waveform Generator Based on LS-SVM and Simulated Annealing Algorithm

2012 ◽  
Vol 268-270 ◽  
pp. 871-874
Author(s):  
Yu Liang Yang ◽  
Jun Qi Qin ◽  
Chang Chun Di ◽  
Yan Feng Yang
Keyword(s):  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Regularization Parameter ◽  
Design Method ◽  
Orthogonal Design ◽  
Structural Parameters ◽  
Parameters Optimization ◽  
Waveform Generator ◽  
Sample Data ◽  
Annealing Algorithm

For the structural design problem of waveform generator, selected diameter of rubber block, hardness and thickness of block 1 and block 2 as five design variables. Firstly, adopted orthogonal design method, and built initial sample data. Secondly, adopted LS-SVM to exercise the sample data, and selected regularization parameter and kernel function width of LS-SVM based on QPSO algorithm. Finally, optimized the structural parameters of waveform generator based on simulated annealing algorithm. The research provided a theoretic basis for the design of waveform generator.

scholarly journals Robust Localization in Distributed MIMO Radar Using Delay and Angle Measurements with Impulsive Noise Robust TD/AOA Localization in Impulsive Noise

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Genling Huang ◽  
Yanlong Zhu
Keyword(s):  
Minimization Problem ◽  
Impulsive Noise ◽  
Target Position ◽  
Mimo Radar ◽  
Optimal Choice ◽  
Position Estimation ◽  
Localization Algorithm ◽  
Angle Of Arrival ◽  
Norm Minimization ◽  
Measurement Equations

This paper considers target localization using time delay (TD) and angle of arrival (AOA) measurements in distributed multiple-input multiple-output (MIMO) radar. Aiming at the problem that the localization performance of existing algorithms degrades sharply in the presence of impulsive noise, we propose a novel localization algorithm based on ℓ p -norm minimization and iteratively reweighted least squares (IRLS). Firstly, the TD and AOA measurement equations are established in the presence of zero-mean symmetric α-stable noise; then, the localization problem is transformed to a ℓ p -norm minimization problem by linearizing the measurement equations; and finally, the ℓ p -norm minimization problem is solved using IRLS by which the target position estimate is obtained, and the optimal choice of norm order p is deduced. Moreover, the Cramér–Rao bound (CRB) for target position estimation in impulsive noise is also derived, generalizing the Gaussian CRB. Simulation results demonstrate that the proposed algorithm outperforms existing algorithms in terms of localization accuracy and robustness in impulsive noise.

Sign in / Sign up

Export Citation Format

Share Document