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Related Concept Videos

Relative Frequency Histogram01:14

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. Like the histogram, a relative frequency histogram also has the same shape with a horizontal scale (the x-axis), but the vertical scale (the y-axis) is marked with relative frequencies (percentages of the whole) instead of actual frequencies. A relative frequency histogram is a graphical representation of a frequency distribution where the...
Histogram01:05

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data represents (for instance, distance from your home to school). The vertical y-axis is labeled either frequency or relative frequency (or percent frequency or probability).
A histogram graph consists of contiguous (adjoining) boxes. The heights of the bars correspond to frequency values. The graph will have the same shape with respective labels. The...
Construction of Frequency Distribution01:15

Construction of Frequency Distribution

A frequency distribution table can be constructed using the steps given below.
First, make a table with two columns—one with the title of the data that needs to be organized, and the other column for frequency. [Draw a third column for tally marks if needed]. Then, take a look at the items given in the data set and decide if an ungrouped frequency distribution table or a grouped frequency distribution table would be more suitable. If there are large sets of different values, then it is best to...
Relative Frequency Distribution00:55

Relative Frequency Distribution

A relative frequency distribution is the proportion or fraction of times a value occurs in a data set. To find the relative frequencies, one can divide each frequency by the total number of data points in the sample. It is very similar to a regular frequency distribution, except that instead of reporting how many data values fall in a class, a relative frequency distribution reports the fraction of data values that fall in a class. These fractions or proportions are called relative frequencies...
Ogive Graph01:07

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, the cumulative percentages are added to the graph from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries along the horizontal x-axis. It’s very similar to a histogram; only instead of rectangles, an ogive displays a single point where the top right of the rectangle would be. Creating this type...
What is a Frequency Distribution00:51

What is a Frequency Distribution

A frequency is the number of times a value of the data occurs. The sum of all the frequency values represents the total number of students included in the sample. It is commonly used to group data of quantitative types. Frequency distributions can be displayed in a table, histogram, line graph, dot plot, or pie chart, just to name a few. A histogram is a graphical representation of tabulated frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), with an area equal to...

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Observation of Photobehavior in Chlamydomonas reinhardtii
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Planogram rebinning with the frequency-distance relationship.

Kyle Champley1, Michel Defrise, Rolf Clackdoyle

  • 1Department of Radiology, University of Washington, Seattle, WA 98195, USA. champlk@u.washington.edu

IEEE Transactions on Medical Imaging
|July 5, 2008
PubMed
Summary
This summary is machine-generated.

We developed an efficient rebinning algorithm for positron emission tomography (PET) systems using panel detectors. This new method improves data processing in 3D imaging by extending existing 2D techniques.

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Area of Science:

  • Medical Imaging
  • Nuclear Medicine
  • Computer Science

Background:

  • Positron Emission Tomography (PET) systems with panel detectors generate data in a native planogram format.
  • Efficient data processing is crucial for accurate and timely image reconstruction in PET.
  • Existing rebinning algorithms may not be optimal for the specific data format of panel detector systems.

Purpose of the Study:

  • To present an efficient rebinning algorithm tailored for PET systems utilizing panel detectors.
  • To adapt the 2D linogram transform for 3D data acquired by panel detectors.
  • To provide theoretical error bounds and validate the algorithm with numerical results.

Main Methods:

  • The rebinning algorithm is derived within the planogram coordinate system.
  • The method is presented as a 3-D extension of the 2-D linogram transform.
  • Theoretical error analysis and numerical simulations were employed for evaluation.

Main Results:

  • The proposed algorithm offers efficient rebinning for PET data from panel detectors.
  • The algorithm successfully extends the 2D linogram transform to 3D.
  • Numerical results demonstrate the algorithm's performance and provide error bounds.

Conclusions:

  • The developed rebinning algorithm is efficient for PET systems with panel detectors.
  • The planogram-based approach simplifies and optimizes data handling.
  • This work contributes to improved image reconstruction in advanced PET systems.