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Related Concept Videos

Median01:08

Median

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Besides mean, the median is a widely used measure of central tendency. Typically, median is defined as the central or middle value of a data set, measured by arranging the data elements in an increasing or decreasing order. Since this middle value is not affected by the precise numerical values of the outliers or fluctuations, it is insensitive to them. Hence, in cases where a data set may have outliers or the extreme values are not known, the median is a better measure of the central tendency...
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Measures of Central Tendency02:16

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The "center" of a data set is also a way of describing location. The two most widely used measures of the "center" of the data are the mean (average) and the median. The words "mean" and "average" are often used interchangeably. The substitution of one word for the other is common practice. The technical term is "arithmetic mean" and "average" is technically a center location. However, in practice among non-statisticians,...
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Sign Test for Median of Single Population01:20

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In general, the sign test serves as a nonparametric method to test hypotheses about the median of a single population when the data does not follow a known distribution. This simplicity makes it particularly useful for small sample sizes or when the assumptions of parametric tests cannot be met. The process begins with identifying a null hypothesis, typically stating that the population median equals a specific value. The alternative hypothesis could be that the median is either not equal to,...
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Wilcoxon Signed-Ranks Test for Median of Single Population01:14

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The Wilcoxon signed-rank test for the median of a single population is a nonparametric test used to evaluate whether the median of a population differs from a specified value. Unlike parametric tests, it does not require data to follow a normal distribution, making it suitable for non-normal or small samples. The test begins by calculating the difference (d) between each observation and the hypothesized median. The absolute values of these differences are ranked in ascending order, with ties...
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Midrange01:07

Midrange

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A somewhat easy to compute quantitative estimate of a data set’s central tendency is its midrange, which is defined as the mean of the minimum and maximum values of an ordered data set.
Simply put, the midrange is half of the data set’s range. Similar to the mean, the midrange is sensitive to the extreme values and hence the prospective outliers. However, unlike the mean, the midrange is not sensitive to all the values of the data set that lie in the middle. Thus, it is prone to...
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Midpoint Rule01:20

Midpoint Rule

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Approximating areas under curved boundaries is a common problem in applied mathematics, particularly when an exact calculation is difficult or impractical. One effective numerical method for this purpose is the Midpoint Rule, which provides an estimate of the area under a curve by using rectangular approximations over a specified interval.Description of the Midpoint RuleThe Midpoint Rule begins by dividing the given interval into a number of equal subintervals. For each subinterval, the...
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Quantifying Intermembrane Distances with Serial Image Dilations
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Non-Local Euclidean Medians.

Kunal N Chaudhury1, Amit Singer2

  • 1Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, NJ 08544 USA.

IEEE Signal Processing Letters
|May 13, 2014
PubMed
Summary
This summary is machine-generated.

The Non-Local Euclidean Medians (NLEM) algorithm improves image denoising at high noise levels by using the median instead of the mean, offering better performance, especially near edges.

Keywords:
Euclidean medianWeiszfeld algorithmimage denoisingiteratively reweighted least squares (IRLS)non-local means

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Area of Science:

  • Image processing
  • Computer vision
  • Signal processing

Background:

  • Non-Local Means (NLM) is a common image denoising algorithm.
  • NLM's performance can degrade at high noise levels.
  • The mean is sensitive to outliers in noisy data.

Purpose of the Study:

  • To introduce a novel denoising algorithm, Non-Local Euclidean Medians (NLEM).
  • To enhance the robustness of Non-Local Means (NLM) denoising.
  • To improve performance at large noise levels and near image edges.

Main Methods:

  • Replacing the mean with the Euclidean median in the NLM framework.
  • Utilizing the median's robustness to outliers.
  • Efficient implementation via iteratively reweighted least squares.

Main Results:

  • NLEM demonstrates improved denoising performance compared to NLM at high noise levels.
  • Geometric insights explain NLEM's superior performance near edges.
  • Computational complexity of NLEM is comparable to NLM.

Conclusions:

  • The Non-Local Euclidean Medians (NLEM) algorithm offers a robust alternative for image denoising.
  • NLEM is particularly effective in challenging conditions with high noise and complex image structures.
  • The proposed method provides a significant advancement in image denoising techniques.