6 research outputs found

    MUPen2DTool: A new Matlab Tool for 2D Nuclear Magnetic Resonance relaxation data inversion

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    A great variety of applications requires to process two-dimensional NMR (2DNMR) data to obtain information about the materials properties. In order to face the increasing request for software to easily process 2DNMR data, in (Bortolotti et al. (2019) [1]), the authors released Upen2dTool, an open source MATLAB software tool implementing nonnegatively constrained uniform penalty locally adapted norm-based regularization for 2DNMR data inversion. This paper presents MUPen2DTool a new open-source MATLAB software tool implementing an unconstrained multipenalty regularization method based on and norms. The new software MUPen2DTool outperforms Upen2dTool since the implemented uniform multipenalty method allows to compute very accurate 2DNMR data inversion at reduced computational cost. By means of MUPen2DTool, the user can choose among several types of NMR experiments, and the free software provides codes that can be used and extended easily. Furthermore, a MATLAB interface makes it easier to include users own data. The practical use is demonstrated in the reported examples of both synthetic and real NMR data

    Limited memory restarted l(p)-l(q) minimization methods using generalized Krylov subspaces

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    Regularization of certain linear discrete ill-posed problems, as well as of certain regression problems, can be formulated as large-scale, possibly nonconvex, minimization problems, whose objective function is the sum of the p(th) power of the l(p)-norm of a fidelity term and the qth power of the lq-norm of a regularization term, with 0 < p,q = 2. We describe new restarted iterative solution methods that require less computer storage and execution time than the methods described by Huang et al. (BIT Numer. Math. 57,351-378, 14). The reduction in computer storage and execution time is achieved by periodic restarts of the method. Computed examples illustrate that restarting does not reduce the quality of the computed solutions

    Uniform multi-penalty regularization for linear ill-posed inverse problems

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    This study examines, in the framework of variational regularization methods, a multi-penalty regularization approach which builds upon the Uniform PENalty (UPEN) method, previously proposed by the authors for Nuclear Magnetic Resonance (NMR) data processing. The paper introduces two iterative methods, UpenMM and GUpenMM, formulated within the Majorization-Minimization (MM) framework. These methods are designed to identify appropriate regularization parameters and solutions for linear inverse problems utilizing multi-penalty regularization. The paper demonstrates the convergence of these methods and illustrates their potential through numerical examples in one and two-dimensional scenarios, showing the practical utility of point-wise regularization terms in solving various inverse problems
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