Correction to: Analysis of the Regularization Parameters of Primal–Dual Interior Method for Convex Objectives Applied to 1H Low Field Nuclear Magnetic Resonance Data Processing

A crucial issue in two-dimensional Nuclear Magnetic Resonance (NMR) is the speed and accuracy of the data inversion. This paper proposes a multi-penalty method with locally adapted regularization parameters for fast and accurate inversion of 2DNMR data.The method solves an unconstrained optimization problem whose objective contains a data-fitting term, a single L1 penalty parameter and a multiple parameter L2 penalty. We propose an adaptation of the Fast Iterative Shrinkage and Thresholding (FISTA) method to solve the multipenalty minimization problem, and an automatic procedure to compute all the penalty parameters. This procedure generalizes the Uniform Penalty principle introduced in [Bortolotti et al., Inverse Problems, 33(1), 2016].The proposed approach allows us to obtain accurate relaxation time distributions while keeping short the computation time. Results of numerical experiments on synthetic and real data prove that the proposed method is efficient and effective in reconstructing the peaks and the flat regions that usually characterize NMR relaxation time distributions.

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2DNMR data inversion using locally adapted multi-penalty regularization

Bortolotti

Landi

Zama

2020

Preprint

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Correction to: Analysis of the Regularization Parameters of Primal–Dual Interior Method for Convex Objectives Applied to 1H Low Field Nuclear Magnetic Resonance Data Processing

Abstract: In the original publication, the acknowledgment section was not published and it is given below now.

Cited by 1 publication

References 13 publications

2DNMR data inversion using locally adapted multi-penalty regularization

2DNMR data inversion using locally adapted multi-penalty regularization

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