scholarly journals A Class of Weighted Low Rank Approximation of the Positive Semidefinite Hankel Matrix

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Jianchao Bai ◽  
Xuefeng Duan ◽  
Kexin Cheng ◽  
Xuewei Zhang
Keyword(s):  
Unconstrained Optimization ◽  
Optimization Problem ◽  
Hankel Matrix ◽  
Positive Semidefinite ◽  
Gradient Algorithm ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Unconstrained Optimization Problem ◽  
Nonlinear Conjugate Gradient ◽  
Rank Approximation

We consider the weighted low rank approximation of the positive semidefinite Hankel matrix problem arising in signal processing. By using the Vandermonde representation, we firstly transform the problem into an unconstrained optimization problem and then use the nonlinear conjugate gradient algorithm with the Armijo line search to solve the equivalent unconstrained optimization problem. Numerical examples illustrate that the new method is feasible and effective.

Application of Structured Low Rank Approximation Method for Noise Elimination from Measured Impulsive Response Functions

2011 ◽  
Vol 48-49 ◽  
pp. 261-264
Author(s):  
Cui Lin Li ◽  
Xing Xian Bao
Keyword(s):  
Numerical Study ◽  
Hankel Matrix ◽  
Low Rank ◽  
Response Functions ◽  
Noise Elimination ◽  
Low Rank Approximation ◽  
Impulsive Response ◽  
Rank Approximation ◽  
Structured Low Rank Approximation ◽  
Elimination Scheme

This paper develops a structured low rank approximation (SLRA) method for noise elimination from a noisy impulsive response function (IRF). Cadzow’s algorithm is implemented for the SLRA on the Hankel matrix constructed by measured IRF in order to obtain a filtered IRF. Using the proposed noise elimination scheme, some important factors, such as the size of a Hankel matrix and the quantification of the noise reduction performance are evaluated. Synthesized IRFs are applied to demonstrate the performance, and illustrate the procedure as well, of the proposed scheme in the numerical study. The results indicate that this method can eliminate noise from measured IRFs efficiently.

scholarly journals A New Conjugate Gradient Algorithm with Sufficient Descent Property for Unconstrained Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
XiaoPing Wu ◽  
LiYing Liu ◽  
FengJie Xie ◽  
YongFei Li
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Gradient Algorithm ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problem ◽  
Nonlinear Conjugate Gradient ◽  
Sufficient Descent ◽  
Descent Condition ◽  
Wolfe Line Search

A new nonlinear conjugate gradient formula, which satisfies the sufficient descent condition, for solving unconstrained optimization problem is proposed. The global convergence of the algorithm is established under weak Wolfe line search. Some numerical experiments show that this new WWPNPRP+algorithm is competitive to the SWPPRP+algorithm, the SWPHS+algorithm, and the WWPDYHS+algorithm.

Improved MR image denoising via low- rank approximation and Laplacian-of-Gaussian edge detector

2020 ◽  
Vol 14 (12) ◽  
pp. 2791-2798
Author(s):  
Xiaoqun Qiu ◽  
Zhen Chen ◽  
Saifullah Adnan ◽  
Hongwei He
Keyword(s):  
Image Denoising ◽  
Low Rank ◽  
Edge Detector ◽  
Low Rank Approximation ◽  
Mr Image ◽  
Rank Approximation
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