A weighted singular value decomposition for the discrete inverse problems

2017 ◽  
Vol 25 (1) ◽  
pp. e2114 ◽  
Author(s):  
Meisam Jozi ◽  
Saeed Karimi
Keyword(s):  
Singular Value Decomposition ◽  
Inverse Problems ◽  
Singular Value ◽  
Value Decomposition ◽  
Weighted Singular Value Decomposition

scholarly journals CRITIQUE OF SOLUTIONS IN LINEARIZED INVERSE PROBLEMS: NUMERICAL EXPERIMENTS IN TRAVELTIME TOMOGRAPHY

2017 ◽  
Vol 34 (4) ◽  
Author(s):  
Silvia L. Bejarano ◽  
Amin Bassrei
Keyword(s):  
Singular Value Decomposition ◽  
Inverse Problems ◽  
Numerical Experiments ◽  
Singular Value ◽  
Traveltime Tomography ◽  
Value Decomposition

ABSTRACT. In this work, we evaluated the quality of the solution of numerical experiments in traveltime tomography, in linear and linearized cases, using singular value decomposition. The simulations were performed using...Keywords: inverse problems, traveltime tomography, resolution matrices, Barbieri method, regularization. RESUMO. Neste trabalho avaliamos a qualidade da solução em experimentos numéricos em tomografia de tempo de trânsito, nos casos linear e linearizado, utilizando o método de decomposição por valores singulares...Palavras-chave: problemas inversos, tomografia de tempos de trânsito, matrizes de resolução, método de Barbieri, regularização.

scholarly journals Enhancing Detection Performance of the Phase-Sensitive OTDR Based Distributed Vibration Sensor Using Weighted Singular Value Decomposition

2021 ◽  
Vol 11 (4) ◽  
pp. 1928
Author(s):  
Khurram Naeem ◽  
Bok Hyeon Kim ◽  
Dong-Jin Yoon ◽  
Il-Bum Kwon
Keyword(s):  
Singular Value Decomposition ◽  
Random Noise ◽  
Time Domain Reflectometry ◽  
Detection Performance ◽  
Singular Value ◽  
Location Information ◽  
Rayleigh Backscattering ◽  
Phase Sensitive ◽  
Value Decomposition ◽  
Weighted Singular Value Decomposition

We propose a weighted singular value decomposition (WSVD) to reduce the random noise in the Rayleigh backscattering signal of the phase-sensitive optical time domain reflectometry (Φ-OTDR) to enhance the detection performance of the distributed vibration sensing. A 2D image is formed by assembling the raw Rayleigh backscattering traces into a matrix form, and slowly varying fluctuation and random noise can be removed using the WSVD. Consequently, the location information and the frequency of vibration induced by the external vibration event can be extracted. A vibration event with 9 m spatial resolution is detected along a 2.4 km single mode fiber. The signal-to-noise ratio (SNR) of location information for the 102 Hz physical vibration and the 525 Hz acoustic vibration was found to be 10.7 and 12.2 dB, respectively. The SNR of the vibration events demonstrate an increase of 6–7 dB compared to the conventional method, showing the excellent denoising capability of this new approach.

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