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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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Accelerators in concrete serve as admixtures to speed up the hardening process, enabling the concrete to achieve early strength faster. Although accelerators do not necessarily impact the time it takes concrete to set, they reduce this time in practice. A common accelerator is calcium chloride, which is particularly useful for hastening early strength development in cold weather or for rapid repair jobs that require quick heat generation after mixing.
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Uncertainty in Measurement: Significant Figures03:34

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All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.
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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Updated: Feb 7, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
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Pixelwise Uncertainty Quantification of Accelerated MRI Reconstruction.

Ilias I Giannakopoulos1, Lokesh B Gautham Muthukumar1,2, Yvonne W Lui1,3

  • 1Bernard and Irene Schwartz Center for Biomedical Imaging, Department of Radiology, NYU Grossman School of Medicine, 10016, New York, NY, United States of America.

Arxiv
|February 6, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a novel framework for quantifying pixel-wise uncertainty in parallel MRI reconstructions. This method automatically identifies unreliable image regions, improving diagnostic reliability without needing reference images.

Keywords:
Conformal PredictionMagnetic Resonance ImagingParallel ImagingQuantile RegressionUncertainty Quantification

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Area of Science:

  • Medical Imaging
  • Machine Learning
  • Image Reconstruction

Background:

  • Parallel imaging accelerates MRI scans but increases reconstruction artifacts as acceleration factor rises.
  • Current clinical practice uses conservative acceleration factors due to the lack of automated methods to assess reconstruction quality.

Purpose of the Study:

  • To develop a general framework for pixel-wise uncertainty quantification in parallel MRI.
  • To enable automatic identification of unreliable regions in undersampled reconstructions without ground-truth data.

Main Methods:

  • Integration of conformal quantile regression with image reconstruction techniques.
  • Development of a Variational Network for end-to-end reconstruction of Cartesian undersampled brain and knee data (acceleration factors 2-10).

Main Results:

  • High agreement (Pearson correlation >90% at 4x acceleration) between predicted uncertainty maps and true reconstruction error.
  • Uncertainty maps accurately capture the magnitude and spatial distribution of reconstruction errors, highlighting artifacts and pathologies.
  • Demonstrated superior performance compared to heuristic residual-based uncertainty estimation.

Conclusions:

  • The proposed framework provides statistically rigorous, pixel-wise uncertainty quantification for parallel MRI.
  • Enables reliable assessment of reconstruction quality without fully-sampled reference images.
  • Paves the way for adaptive MRI protocols balancing scan time and diagnostic accuracy.