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Related Concept Videos

Sampling Plans01:23

Sampling Plans

233
Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

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Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
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Stratified Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Cluster Sampling Method01:20

Cluster Sampling Method

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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Convenience Sampling Method00:55

Convenience Sampling Method

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Random Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
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Updated: Aug 12, 2025

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Diffusion sampling schemes: A generalized methodology with nongeometric criteria.

Justino R Rodríguez-Galván1, Guillem París1, Antonio Tristán-Vega1

  • 1Laboratorio de Procesado de Imagen (LPI), Universidad de Valladolid, Valladolid, Spain.

Magnetic Resonance in Medicine
|January 27, 2023
PubMed
Summary
This summary is machine-generated.

Geometrical criteria for designing k-space sampling may not yield optimal reconstruction matrices. The proposed WISH method, using weighted shell distances, offers improved performance for magnetic resonance imaging (MRI) reconstruction compared to existing methods.

Keywords:
Voronoicoherencediffusion MRIq-space sampling

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Area of Science:

  • Medical Imaging
  • Signal Processing
  • Computational Science

Background:

  • Designing k-space sampling procedures is crucial for efficient Magnetic Resonance Imaging (MRI).
  • Traditional geometrical criteria for sampling may not directly translate to optimal reconstruction matrix performance in compressed sensing.
  • Existing methods like General Electrostatic Energy Minimization (GEEM) and Spherical Codes (SC) have limitations in optimizing sampling strategies.

Purpose of the Study:

  • To demonstrate that geometrical sampling criteria do not always ensure high-performance reconstruction matrices in compressed sensing.
  • To introduce and evaluate a novel gradient design method, WISH (WeIghting SHells), for multishell k-space sampling.
  • To compare WISH performance against state-of-the-art methods using compressed sensing metrics.

Main Methods:

  • Proposed the WISH method, optimizing an objective function based on weighted distances between gradients in consecutive shells.
  • Utilized Spiral Phyllotaxis as an initialization strategy for optimizing the nonconvex objective function.
  • Compared WISH against GEEM and SC, evaluating reconstruction matrices using Restricted Isometry Property (RIP) and Coherence from compressed sensing theory, and a geometric Voronoi cell criterion.

Main Results:

  • The WISH method achieved superior results for Restricted Isometry Property (RIP) and Coherence metrics in at least one weight combination.
  • A geometric criterion based on Voronoi cells did not show a consistent or related pattern with WISH performance.
  • WISH demonstrated versatility and outperformed existing methods in key compressed sensing figures of merit.

Conclusions:

  • The WISH method provides a versatile approach to designing k-space sampling procedures with improved reconstruction matrix performance.
  • Further optimization within the weight parameter space of WISH is expected to yield additional improvements.
  • The proposed methodology is recommended for practical gradient table design in MRI acquisitions.