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 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.

scholarly journals Implementation of the computer tomography parallel algorithms with the incomplete set of data

2021 ◽  
Vol 7 ◽  
pp. e339
Author(s):  
Mariusz Pleszczyński
Keyword(s):  
Computer Tomography ◽  
Incomplete Data ◽  
Unusual Case ◽  
Linear Equations ◽  
Maximum Error ◽  
Wide Field ◽  
System Of Linear Equations ◽  
Data Set ◽  
Optimal Values ◽  
Block Approach

Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object, satisfy the expectations regarding their amount and quality. Unfortunately, sometimes such expected data cannot be achieved. Then we deal with the incomplete set of data. In the paper we consider an unusual case of such situation, which may occur when the access to the examined object is difficult. The previous research, conducted by the author, showed that the CT algorithms can be used successfully in this case as well, but the time of reconstruction is problematic. One of possibilities to reduce the time of reconstruction consists in executing the parallel calculations. In the analyzed approach the system of linear equations is divided into blocks, such that each block is operated by a different thread. Such investigations were performed only theoretically till now. In the current paper the usefulness of the parallel-block approach, proposed by the author, is examined. The conducted research has shown that also for an incomplete data set in the analyzed algorithm it is possible to select optimal values of the reconstruction parameters. We can also obtain (for a given number of pixels) a reconstruction with a given maximum error. The paper indicates the differences between the classical and the examined problem of CT. The obtained results confirm that the real implementation of the parallel algorithm is also convergent, which means it is useful.

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