Introduction to Healthcare-Oriented Monitoring of Persons

Wagner, Jakub; Mazurek, Paweł; Morawski, Roman Z.

doi:10.1007/978-3-030-96009-4_1

Cited by 2 publications

(2 citation statements)

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“…This kind of instability defines an ill-posed problem that can be solved by applying the Tikhonov regularization theory to stabilize numerical derivatives evaluated from noisy time series or vector data (Eilers, 2003;Stickel, 2010). The regularized derivative procedure was introduced by Cullum (1971) and since then found applications in many fields of the engineering and experimental sciences (Eilers, 2003;Wagner, 2020). The problem can be formulated as a Tikhonov regularization problem (Eilers, 2003;Stickel, 2010).…”

Section: Computational Implementationmentioning

confidence: 99%

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Thin Sheet Automatic Interpretation of Dike Swarm Magnetic Transects Using Regularized Second Derivatives

Mendonça¹,

Cavalcante²,

Melo³

2023

Preprint

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Dike swarms are major continental structures recording large igneous provinces and crustal extension processes generating rifts and sedimentary basins. A key point in dike swarm studies is determining a minimum number of dikes that are necessary to explain the observed magnetic anomalies and inferences about position and depth for specific unities. We develop an automatic interpretation procedure to interpret the complex anomalies resulting from densely juxtaposed dikes forming a swarm, each dike with different depth and magnetization attributes. The automatic parameter estimation is based on the ratio of the amplitude of the magnetic anomaly (AMA) by its second-order derivative, the dike position and depth determined from simple algebraic expressions based on the thin-sheet model representation. The second derivative of the AMA serves to individualize intervals with specific dike units, thereby determining a minimum number of dikes based on their sharp or subtle concave-down expressions in the AMA profile. Tikhonov regularization is applied to prevent noise enhancement in evaluating numerical derivatives using a finite-difference scheme. A set of MATLAB programs are presented to evaluate the automatic interpretation of magnetic transects, a profile across the Ponta Grossa Dike Swarm in Southern Brazil serving as a testing data set since its results can be compared with a published dike model obtained from data inversion. Dike location and depth obtained with the automatic procedure accurately recover the model parameters obtained from nonlinear data inversion suggesting the utility of the proposed procedure to obtain a reliable model from complex anomalies.

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Section: Computational Implementationmentioning

confidence: 99%

“…The problem can be formulated as a Tikhonov regularization problem (Eilers, 2003;Stickel, 2010). Code implementation was done with the MATLAB function rdiff with option for Tikhonov regularization (Wagner, 2020;pg. 79).…”

Section: Computational Implementationmentioning

confidence: 99%