scholarly journals Inverse Multiscale Discrete Radon Transform by Filtered Backprojection

2020 ◽  
Vol 11 (1) ◽  
pp. 22
Author(s):  
José G. Marichal-Hernández ◽  
Ricardo Oliva-García ◽  
Óscar Gómez-Cárdenes ◽  
Iván Rodríguez-Méndez ◽  
José M. Rodríguez-Ramos
Keyword(s):  
Numerical Methods ◽  
Inverse Problems ◽  
Iterative Methods ◽  
Radon Transform ◽  
Discrete Version ◽  
Filtered Backprojection ◽  
Discrete Radon Transform ◽  
First Time ◽  
The Sacrifice ◽  
Iterative Numerical Methods

The Radon transform is a valuable tool in inverse problems such as the ones present in electromagnetic imaging. Up to now the inversion of the multiscale discrete Radon transform has been only possible by iterative numerical methods while the continuous Radon transform is usually tackled with the filtered backprojection approach. In this study, we will show, for the first time, that the multiscale discrete version of Radon transform can as well be inverted with filtered backprojection, and by doing so, we will achieve the fastest implementation until now of bidimensional discrete Radon inversion. Moreover, the proposed method allows the sacrifice of accuracy for further acceleration. It is a well-conditioned inversion that exhibits a resistance against noise similar to that of iterative methods.

scholarly journals Comparative Study of Various Iterative Numerical Methods for Computation of Approximate Root of the Polynomials

2021 ◽  
Vol 11 (2) ◽  
pp. 6-11
Author(s):  
Dr. Roopa K M ◽  
◽  
Venkatesha P ◽  
Keyword(s):  
Numerical Methods ◽  
Comparative Study ◽  
Iterative Methods ◽  
Numerical Comparison ◽  
Polynomial Equations ◽  
Chebyshev Method ◽  
Newton Raphson ◽  
Raphson Method ◽  
Iterative Numerical Methods

The aim of this article is to present a brief review and a numerical comparison of iterative methods applied to solve the polynomial equations with real coefficients. In this paper, four numerical methods are compared, namely: Horner’s method, Synthetic division with Chebyshev method (Proposed Method), Synthetic division with Modified Newton Raphson method and Birge-Vieta method which will helpful to the readers to understand the importance and usefulness of these methods.

scholarly journals The discrete Radon transform and its approximate inversion via linear programming

1997 ◽  
Vol 75 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Peter Fishburn ◽  
Peter Schwander ◽  
Larry Shepp ◽  
Robert J. Vanderbei
Keyword(s):  
Linear Programming ◽  
Radon Transform ◽  
Discrete Radon Transform

XIV. The Pahlavi Texts of the Srosh Yasht with its Introductions, Being Yasna LV-LVI (IN S.B.E. xxxi LVI–LVII), For the First Time Critically Translated.

1905 ◽  
Vol 37 (3) ◽  
pp. 451-469
Author(s):  
Lawrence Mills
Keyword(s):  
The One ◽  
First Time ◽  
The Sacrifice

‘Here be’ (or ‘here is’) this hearing (or ‘this listening to’) the sacrifice of Aūharmazd [that is to say, let him, Srōš (this listening personified), come on to this (our Sacrifice)], a sacrifice to the One wishful for our benefit (sic) (hardly ‘ of the One supplicated for our prosperity’), to the sacrifice of Aūharmazd, the Holy, who is desirous of our (prosperity) as at the first; [the meaning (is) (so I would here translate ‘mēnešnīg’);— the meaning is: ‘as I have now stood at the first thus within this sacrificial (precinct, so here be the hearing of the sacrifice now)], and at the last [so meaning, ‘ I would so complete its end’]. A person here attending is therefore this’ (meaning that every sincere attendant upon the sacrifice should assume the attitude herein above indicated).

scholarly journals Numerical methods for multiscale inverse problems

2017 ◽  
Vol 15 (2) ◽  
pp. 305-328 ◽  
Author(s):  
Christina Frederick ◽  
Björn Engquist
Keyword(s):  
Numerical Methods ◽  
Inverse Problems

scholarly journals Optimization Learning: Perspective, Method, and Applications

2020 ◽  
Author(s):  
Risheng Liu
Keyword(s):  
Inverse Problems ◽  
Theoretical Analysis ◽  
Iterative Methods ◽  
State Of The Art ◽  
Learning Paradigm ◽  
Rigorous Analysis ◽  
The Core ◽  
Globally Convergent ◽  
Ill Posed ◽  
Art Performance

Numerous tasks at the core of statistics, learning, and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems. Nevertheless, integrating learnable structures into iterations is still a laborious process, which can only be guided by intuitions or empirical insights. Moreover, there is a lack of rigorous analysis of the convergence behaviors of these reimplemented iterations, and thus the significance of such methods is a little bit vague. We move beyond these limits and propose a theoretically guaranteed optimization learning paradigm, a generic and provable paradigm for nonconvex inverse problems, and develop a series of convergent deep models. Our theoretical analysis reveals that the proposed optimization learning paradigm allows us to generate globally convergent trajectories for learning-based iterative methods. Thanks to the superiority of our framework, we achieve state-of-the-art performance on different real applications.

The polynomial discrete Radon transform

2014 ◽  
Vol 9 (S1) ◽  
pp. 145-154
Author(s):  
Ines ELouedi ◽  
Régis Fournier ◽  
Amine Naït-Ali ◽  
Atef Hamouda
Keyword(s):  
Radon Transform ◽  
Discrete Radon Transform
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