Application of low‐rank approximation using truncated singular value decomposition for noise reduction in hyperpolarized 13 C NMR spectroscopy

2020 ◽  
Author(s):  
R. Francischello ◽  
M. Geppi ◽  
A. Flori ◽  
E.M. Vasini ◽  
S. Sykora ◽  
...  
Keyword(s):  
Nmr Spectroscopy ◽  
Singular Value Decomposition ◽  
Noise Reduction ◽  
Singular Value ◽  
Low Rank ◽  
Truncated Singular Value Decomposition ◽  
Low Rank Approximation ◽  
Rank Approximation ◽  
Value Decomposition ◽  
C Nmr

A Control Loop Structure Based on Singular Value Decomposition for Input-Coupled Systems

2011 ◽  
Author(s):  
Ryder C. Winck ◽  
Wayne J. Book
Keyword(s):  
Singular Value Decomposition ◽  
Current Control ◽  
Singular Value ◽  
Coupled Systems ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Column System ◽  
Input Design ◽  
Actuator Control ◽  
Value Decomposition

This paper introduces a control structure based on the singular value decomposition (SVD) to control multiple subsystems with reduced inputs. The SVD System permits simultaneous, dependent control of sets of subsystems coupled by a row-column input design. The use of the SVD differs from previous applications because it is used to obtain a low-rank approximation of desired inputs. The row-column system allows many actuators to be controlled by a few inputs. Current control methods using the row-column system rely on scheduling techniques that permit independent actuator control but are too slow for many applications. The inspiration for this new control construct is a pin array human machine interface, called Digital Clay. Some useful properties of the SVD will be discussed and the SVD System will be described and demonstrated in a simulation of Digital Clay.

scholarly journals A modified truncation singular value decomposition method for solving ill-posed problems

2018 ◽  
Vol 13 ◽  
pp. 174830181881360 ◽  
Author(s):  
Zhenyu Zhao ◽  
Riguang Lin ◽  
Zehong Meng ◽  
Guoqiang He ◽  
Lei You ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Decomposition Method ◽  
Singular Value ◽  
Numerical Results ◽  
New Method ◽  
Truncated Singular Value Decomposition ◽  
Singular Value Decomposition Method ◽  
Ill Posed ◽  
Value Decomposition

A modified truncated singular value decomposition method for solving ill-posed problems is presented in this paper, in which the solution has a slightly different form. Both theoretical and numerical results show that the limitations of the classical TSVD method have been overcome by the new method and very few additive computations are needed.

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