Tikhonov regularization using a minimum-product criterion: Application to brain electrical tomography

Author(s):  
E.M. Ventouras ◽  
C.C. Papageorgiou ◽  
N.K. Uzunoglu ◽  
G.N. Christodoulou
2000 ◽  
Vol 14 (1) ◽  
pp. 95-99 ◽  
Author(s):  
E. Ventouras ◽  
C. Papageorgiou ◽  
N. Uzunoglu ◽  
S. Koulouridis ◽  
A. Rabavilas ◽  
...  

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.


2020 ◽  
Vol 12 (1) ◽  
pp. 1094-1104
Author(s):  
Nima Dastanboo ◽  
Xiao-Qing Li ◽  
Hamed Gharibdoost

AbstractIn deep tunnels with hydro-geological conditions, it is paramount to investigate the geological structure of the region before excavating a tunnel; otherwise, unanticipated accidents may cause serious damage and delay the project. The purpose of this study is to investigate the geological properties ahead of a tunnel face using electrical resistivity tomography (ERT) and tunnel seismic prediction (TSP) methods. During construction of the Nosoud Tunnel located in western Iran, ERT and TSP 303 methods were employed to predict geological conditions ahead of the tunnel face. In this article, the results of applying these methods are discussed. In this case, we have compared the results of the ERT method with those of the TSP 303 method. This work utilizes seismic methods and electrical tomography as two geophysical techniques are able to detect rock properties ahead of a tunnel face. This study shows that although the results of these two methods are in good agreement with each other, the results of TSP 303 are more accurate and higher quality. Also, we believe that using another geophysical method, in addition to TSP 303, could be helpful in making decisions in support of excavation, especially in complicated geological conditions.


2021 ◽  
Vol 7 (2) ◽  
pp. 18
Author(s):  
Germana Landi ◽  
Fabiana Zama ◽  
Villiam Bortolotti

This paper is concerned with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) relaxometry. This is a large-scale and ill-posed inverse problem with many potential applications in biology, medicine, chemistry, and other disciplines. However, the large amount of data and the consequently long inversion times, together with the high sensitivity of the solution to the value of the regularization parameter, still represent a major issue in the applicability of the NMR relaxometry. We present a method for two-dimensional data inversion (2DNMR) which combines Truncated Singular Value Decomposition and Tikhonov regularization in order to accelerate the inversion time and to reduce the sensitivity to the value of the regularization parameter. The Discrete Picard condition is used to jointly select the SVD truncation and Tikhonov regularization parameters. We evaluate the performance of the proposed method on both simulated and real NMR measurements.


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