Applications of PDEs inpainting to magnetic particle imaging and corneal topography

Andrisani, Andrea; Mininni, Rosa Maria; Mazzia, Francesca; Settanni, Giuseppina; Iurino, Alessandro; Tangaro, Sabina; Tateo, Andrea; Bellotti, R.

doi:10.7494/opmath.2019.39.4.453

Cited by 4 publications

(3 citation statements)

References 45 publications

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“…The tensor product of the BSH QI is applied using its polar coordinates form, when, during a final step, we regularize the final eye surface. Extended discussion, details and numerical results can be found in [Andrisani et al, 2019].…”

Section: Real World Data Testsmentioning

confidence: 99%

The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation

Bertolazzi¹,

Falini²,

Mazzia³

2022

Preprint

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The library QIBSH++ is a C++ object oriented library for the solution of Quasi Interpolation problems. The library is based on a Hermite Quasi Interpolating operator, which was derived as continuous extensions of linear multistep methods applied for the numerical solution of Boundary Value Problems for Ordinary Differential Equations. The library includes the possibility to use Hermite data or to apply a finite difference scheme for derivative approximations, when derivative values are not directly available. The generalization of the quasi interpolation procedure to surfaces and volumes approximation by means of a tensor product technique is also implemented. The method has been also generalized for one dimensional vectorial data, periodic data, and for two dimensional data in cylindrical coordinates, periodic with respect to the angular argument. Numerical tests show that the library could be used efficiently in many practical problems.

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Section: Real World Data Testsmentioning

confidence: 99%

The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation

Bertolazzi¹,

Falini²,

Mazzia³

2022

Preprint

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“…where ℎ is a reference altitude to be defined, while ℎ ≤ ℎ . For its ability to detect sharp variations of a function, the total variation operator is often used in denoising problems [51], in deconvolution problems [52], in segmentation [53], and in inpainting [54,55]. In general, deviates from when shows non-monotone behavior: then a significative deviation of from could indicate water vapor presence, according to [41] (see Figure 8).…”

Section: Difference Of the Bending Angle From Its Total Variationmentioning

confidence: 99%

Comparisons of Different Methods to Determine Starting Altitudes for Dry Air Atmosphere by GNSS-RO Data

Andrisani

Vespe

2021

Atmosphere

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Boundary profile evaluation (BPV) is an approach proposed in order to estimate water vapor content in the atmosphere. It exploits radio occultation (RO) observations of the signals emitted by the satellites of global navigation systems (GNSS) which are eclipsing (rising) as viewed by a low earth orbit satellite (LEO). BPV requires, as a preliminary step, the estimation of the dry background atmosphere model of refractivity (i.e., obtained from bending angle profiles) to be subtracted from the real observations in order to extract water vapor profiles. The determination of the lowest layer of the atmosphere over which the concentration of water vapor can be deemed negligible is particularly crucial for a correct application of the BPV method. In this study, we have applied three methods to set the starting altitudes for the dry air layers of the atmosphere: (1) by air temperature below some threshold values (for example, 250 K); (2) by “smooth” bending angle profiles in ROs; (3) by saturated water vapor pressure. These methods were tested with thermodynamic and bending angle profiles from 912 radiosonde excursions colocated with RO observations. For every dry air starting altitude we determined the best estimator from each of the three methods. In particular, by comparing those estimators with the quantiles and momenta of the dry air starting altitude distributions, we achieved improvements of up to 50% of the humidity profiles.

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“…This research is based on some work we commenced to collaborate to, trying to merge our research interests. In particular, we recall the works related to saliency and change detection, made in collaboration with Antonella Falini [21,23] and the work related to the inpainting techniques [2], all of them resulting from common projects with local industrial partners. The last section of the paper is devoted to the description of an algorithm based on dynamic copulas, a subject that she was following with extremely interest.…”

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confidence: 99%

Spline based Hermite quasi-interpolation for univariate time series

Falini

Mazzia

Tamborrino

2022

DCDS-S

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<p style='text-indent:20px;'>In this article the authors introduce a spline Hermite quasi-interpolation technique for the preprocessing operations of imputation and smoothing of univariate time series. The constructed model is then applied for the forecast and for the anomaly detection. In particular, for the latter case, algorithms based on the combination of quasi-interpolation, dynamic copulas and clustering have been proposed. Some numerical results are included showing the effectiveness of the presented techniques.</p>

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Applications of PDEs inpainting to magnetic particle imaging and corneal topography

Cited by 4 publications

References 45 publications

The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation

The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation

Comparisons of Different Methods to Determine Starting Altitudes for Dry Air Atmosphere by GNSS-RO Data

Spline based Hermite quasi-interpolation for univariate time series

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