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Related Concept Videos

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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Related Experiment Videos

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models.

J C De Los Reyes1, C-B Schönlieb2, T Valkonen3

  • 11Research Center on Mathematical Modelling (MODEMAT), Escuela Politécnica Nacional, Quito, Ecuador.

Journal of Mathematical Imaging and Vision
|May 2, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a novel bilevel optimization method for parameter learning in higher-order total variation (TV) image reconstruction. The new approach offers improved performance and a detailed comparison of different regularizers for enhanced image processing.

Keywords:
Bilevel optimisationImage quality measuresTotal variation regularisers

Related Experiment Videos

Area of Science:

  • Applied Mathematics
  • Image Processing
  • Optimization Theory

Background:

  • Higher-order total variation (TV) models are crucial for image reconstruction.
  • Parameter learning in these models is essential for optimal performance.
  • Existing bilevel learning approaches often rely on least squares cost functionals.

Purpose of the Study:

  • To develop and analyze a bilevel optimization approach for parameter learning in higher-order TV image reconstruction.
  • To introduce and evaluate an alternative cost functional based on a Huber-regularized TV seminorm.
  • To provide a comprehensive comparison of different regularizers within the bilevel framework.

Main Methods:

  • Bilevel optimization framework for parameter learning.
  • Analysis of differentiability properties of the solution operator.
  • Derivation of a first-order optimality system.
  • Development of a combined quasi-Newton/semismooth Newton algorithm.
  • Numerical experiments for performance evaluation.

Main Results:

  • Verification of differentiability properties and derivation of optimality conditions.
  • Successful implementation of a combined quasi-Newton/semismooth Newton algorithm.
  • Demonstration of the suitability of the proposed bilevel optimization approach.
  • Evidence of improved performance with the new Huber-regularized TV seminorm cost functional.
  • Detailed comparison of and regularizers, highlighting their respective advantages and limitations based on image characteristics and noise levels.

Conclusions:

  • The proposed bilevel optimization approach effectively handles parameter learning in higher-order TV image reconstruction.
  • The novel Huber-regularized TV seminorm cost functional enhances reconstruction performance.
  • The framework facilitates a nuanced understanding of different regularizers for image processing applications.