Numerical Method for Solving 3D Inverse Problems with Complete and Incomplete Data

1989 ◽  
pp. 34-43 ◽  
Author(s):  
Alexander G. Ramm
Keyword(s):  
Inverse Problems ◽  
Numerical Method ◽  
Incomplete Data

scholarly journals Assessing the Credibility of the Solutions of Incomplete-Data Inverse Problems

Physics Open ◽  
2021 ◽  
pp. 100074
Author(s):  
Aydin M. Torkabadi ◽  
Esam M.A. Hussein
Keyword(s):  
Inverse Problems ◽  
Incomplete Data

scholarly journals A Convex Variational Model for Learning Convolutional Image Atoms from Incomplete Data

2019 ◽  
Vol 62 (3) ◽  
pp. 417-444
Author(s):  
A. Chambolle ◽  
M. Holler ◽  
T. Pock
Keyword(s):  
Image Reconstruction ◽  
Inverse Problems ◽  
Incomplete Data ◽  
Variational Model ◽  
Well Posedness ◽  
Optimal Solutions ◽  
Analytical Properties ◽  
Numerical Performance ◽  
Stability Results ◽  
Continuous Setting

AbstractA variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is convex and allows for simultaneous image reconstruction and atom learning in a general, inverse problems context. Further, motivated by an improved numerical performance, also a semi-convex variant is included in the analysis and the experiments of the paper. For both settings, fundamental analytical properties allowing in particular to ensure well-posedness and stability results for inverse problems are proven in a continuous setting. Exploiting convexity, globally optimal solutions are further computed numerically for applications with incomplete, noisy and blurry data and numerical results are shown.

Inverse problems of computer tomography with incomplete data

1991 ◽  
Vol 2 (1) ◽  
pp. 61-63
Author(s):  
A. N. Matvienko ◽  
T. N. Novikova
Keyword(s):  
Inverse Problems ◽  
Computer Tomography ◽  
Incomplete Data

scholarly journals NUMERICAL METHOD FOR THE SOLUTION OF INVERSE PROBLEMS GENERATED BY PERTURBATIONS OF SELF-ADJOINT OPERATORS BY METHOD OF REGULARIZED TRACES

2017 ◽  
Vol 19 (6) ◽  
pp. 23-30
Author(s):  
S.I. Kadchenko
Keyword(s):  
Inverse Problems ◽  
Numerical Method ◽  
Computational Efficiency ◽  
Spectral Characteristics ◽  
New Method ◽  
Sturm Liouville ◽  
Adjoint Operators

In the article a new method for the solution of inverse problems generated by perturbations of self-adjoint operators on their spectral characteristics is developed. The method was tested on inverse problems for Sturm-Liouville problems. The results of numerous calculations showed the computational efficiency of the method.

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