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Related Concept Videos

Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

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.
For data that follow a straight line, the standard method for fitting is the linear...
Instrument Calibration01:12

Instrument Calibration

Instrument calibration is essential for ensuring that instruments produce accurate and consistent results. It is vital in manufacturing, healthcare, testing laboratories, and scientific research. Calibration processes are specific to each instrument and help enhance data accuracy. Each instrument has a unique calibration process tailored to its design and function to improve data accuracy.
Analytical Balance Calibration
An analytical balance measures mass and requires regular calibration to...
Gravimetry: Overview01:05

Gravimetry: Overview

Gravimetric analysis is a quantitative method where the analyte is isolated and weighed directly or after conversion into a substance of known composition. Gravimetric analysis can be classified as precipitation, electrogravimetry, volatilization, and particulate gravimetry, based on the method used to isolate the analyte.
In precipitation gravimetry, the analyte is converted into a precipitate and weighed. For example, the silver content in a sample can be estimated by precipitating and...
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...

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Related Experiment Video

Updated: May 30, 2026

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression
11:26

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression

Published on: December 10, 2014

A radial self-calibrated (RASCAL) generalized autocalibrating partially parallel acquisition (GRAPPA) method using

Noel C F Codella1, Pascal Spincemaille, Martin Prince

  • 1Department of Physiology, Biophysics and Systems Biology, Weill Medical College of Cornell University, New York, NY, USA.

NMR in Biomedicine
|August 12, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a new generalized autocalibrating partially parallel acquisition (GRAPPA) method for radial imaging. It enables GRAPPA weight calculation without calibration data, improving image reconstruction for radial k-space sampling.

Related Experiment Videos

Last Updated: May 30, 2026

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression
11:26

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression

Published on: December 10, 2014

Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Image Reconstruction
  • Medical Physics

Background:

  • Generalized Autocalibrating Partially Parallel Acquisition (GRAPPA) is a key technique in MRI for accelerating data acquisition.
  • Radial k-space sampling offers advantages but presents challenges for traditional GRAPPA methods.
  • Existing self-calibrated GRAPPA techniques for radial trajectories have limitations.

Purpose of the Study:

  • To develop and validate a novel GRAPPA method for radial k-space sampling that eliminates the need for separate calibration data.
  • To enable accurate GRAPPA weight calculation directly from undersampled radial data.
  • To improve image reconstruction quality in undersampled radial MRI.

Main Methods:

  • A generalized autocalibrating partially parallel acquisition (GRAPPA) method was developed for radial k-space sampling.
  • GRAPPA weights were fitted directly to undersampled radial data, bypassing the need for acquired or synthesized calibration scans.
  • A novel resampling strategy using interpolation was employed to adapt GRAPPA weights for varying k-space shifts inherent in radial trajectories, generating missing projections.

Main Results:

  • The proposed method successfully calculated GRAPPA weights without calibration data.
  • Demonstrated feasibility in phantom, abdominal, and brain imaging.
  • Achieved image quality comparable to conventional radial GRAPPA with fully sampled calibration data.
  • Showed improved image quality compared to a prior self-calibrated radial GRAPPA technique.

Conclusions:

  • The developed method offers an effective approach for autocalibrating GRAPPA in radial MRI, removing the need for calibration data.
  • This technique enhances image reconstruction for undersampled radial trajectories, particularly in applications like abdominal and brain imaging.
  • The findings suggest a significant advancement in accelerated radial MRI acquisition and reconstruction.