Electrocardiographic Imaging in Atrial Fibrillation: Selection of the Optimal Tikhonov-Regularization Parameter

The present paper is concerned with developing tensor iterative Krylov subspace methods to solve large multi-linear tensor equations. We use the T-product for two tensors to define tensor tubal global Arnoldi and tensor tubal global Golub-Kahan bidiagonalization algorithms. Furthermore, we illustrate how tensor-based global approaches can be exploited to solve ill-posed problems arising from recovering blurry multichannel (color) images and videos, using the so-called Tikhonov regularization technique, to provide computable approximate regularized solutions. We also review a generalized cross-validation and discrepancy principle type of criterion for the selection of the regularization parameter in the Tikhonov regularization. Applications to image sequence processing are given to demonstrate the efficiency of the algorithms.

Download Full-text

Selection of Antithrombotic Therapy in Patients with Atrial Fibrillation and Percutaneous Coronary Intervention

Current Pharmaceutical Design ◽

10.2174/1381612822666160623070130 ◽

2016 ◽

Vol 22 (29) ◽

pp. 4604-4609

Author(s):

Theodoros A. Zografos ◽

Demosthenes G. Katritsis

Keyword(s):

Atrial Fibrillation ◽

Percutaneous Coronary Intervention ◽

Antithrombotic Therapy ◽

Coronary Intervention ◽

Percutaneous Coronary ◽

Selection Of

Download Full-text

The impact of left atrium size on selection of the pulmonary vein isolation method for atrial fibrillation: Cryoballoon or radiofrequency catheter ablation

American Heart Journal ◽

10.1016/j.ahj.2020.10.061 ◽

2021 ◽

Vol 231 ◽

pp. 82-92

Author(s):

Takashi Ikenouchi ◽

Osamu Inaba ◽

Tomomasa Takamiya ◽

Yukihiro Inamura ◽

Akira Sato ◽

...

Keyword(s):

Atrial Fibrillation ◽

Catheter Ablation ◽

Left Atrium ◽

Pulmonary Vein ◽

Pulmonary Vein Isolation ◽

Radiofrequency Catheter Ablation ◽

Isolation Method ◽

The Impact ◽

Left Atrium Size ◽

Selection Of

Download Full-text

A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

Open Mathematics ◽

10.1515/math-2020-0111 ◽

2020 ◽

Vol 18 (1) ◽

pp. 1685-1697

Author(s):

Zhenyu Zhao ◽

Lei You ◽

Zehong Meng

Keyword(s):

Cauchy Problem ◽

Laplace Equation ◽

Tikhonov Regularization ◽

Regularization Method ◽

Regularization Parameter ◽

Solution Process ◽

Tikhonov Regularization Method ◽

Hermite Expansion ◽

The Cauchy Problem ◽

Ill Posed

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.

Download Full-text

A New Hybrid Inversion Method for 2D Nuclear Magnetic Resonance Combining TSVD and Tikhonov Regularization

Journal of Imaging ◽

10.3390/jimaging7020018 ◽

2021 ◽

Vol 7 (2) ◽

pp. 18

Author(s):

Germana Landi ◽

Fabiana Zama ◽

Villiam Bortolotti

Keyword(s):

Nuclear Magnetic Resonance ◽

Magnetic Resonance ◽

Tikhonov Regularization ◽

Large Scale ◽

Regularization Parameter ◽

High Sensitivity ◽

Inversion Method ◽

Nmr Relaxometry ◽

Value Decomposition ◽

Nuclear Magnetic

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.

Download Full-text