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Time and frequency -Domain Interpretation of Phase-lead Control01:24

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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Related Experiment Video

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A comprehensive numerical analysis of background phase correction with V-SHARP.

Pinar Senay Özbay1,2, Andreas Deistung3, Xiang Feng3,4

  • 1Institute of Diagnostic and Interventional Radiology, University Hospital Zurich and University of Zurich, Zurich, Switzerland.

NMR in Biomedicine
|June 4, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a new generalized parameter scheme for Sophisticated Harmonic Artifact Reduction for Phase data (SHARP) in MRI. The novel approach simplifies parameter selection for improved quantitative susceptibility mapping (QSM) accuracy.

Keywords:
background field removalphasequantitative susceptibility mapping (QSM)sophisticated harmonic artifact reduction for phase data (SHARP)

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Area of Science:

  • Medical Imaging
  • Magnetic Resonance Imaging (MRI)
  • Image Processing

Background:

  • Sophisticated Harmonic Artifact Reduction for Phase data (SHARP) is crucial for quantitative susceptibility mapping (QSM) by removing background field contributions in MRI phase images.
  • Current SHARP methods require defining a spherical kernel radius and a regularization parameter, which can be dependent on acquisition and processing characteristics.
  • This dependence complicates standardized application and optimization of SHARP.

Purpose of the Study:

  • To analyze the impact of SHARP's spherical kernel radius and regularization parameter on corrected MRI phase images and reconstructed susceptibility maps.
  • To propose and validate a new, generalized SHARP parameter scheme that simplifies and standardizes parameter selection.
  • To enhance the robustness and accuracy of quantitative susceptibility mapping (QSM) through improved artifact reduction.

Main Methods:

  • Extensive analysis of SHARP parameter effects using a numerical brain model with the variable-kernel SHARP (V-SHARP) approach.
  • Systematic variation of maximum radii (Rm) from 1 to 15 mm and regularization parameters (f).
  • Development of a new SHARP scheme utilizing a high-pass filtering approach to determine the regularization parameter, validated in vivo.

Main Results:

  • Local root-mean-square error (RMSE) in background-corrected field maps decreased towards the brain's center.
  • Optimal RMSE for susceptibility maps varied based on the calculation algorithm: spatial domain (Rm: 6-10 mm, f: 0-0.01 mm-1) and Fourier domain (Rm: 10-15 mm, f: 0-0.0091 mm-1).
  • The proposed generalized parameter scheme was successfully demonstrated and confirmed in vivo, showing consistent performance across different imaging parameters.

Conclusions:

  • The new SHARP regularization scheme enables the use of a single, consistent regularization parameter regardless of imaging parameters like resolution.
  • This generalization simplifies the application of SHARP, leading to more reliable and accurate quantitative susceptibility mapping (QSM).
  • The findings provide a more robust and user-friendly method for artifact reduction in MRI phase imaging.