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Related Concept Videos

Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

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...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Cluster Sampling Method01:20

Cluster Sampling Method

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.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

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Using the GRAPPA operator and the generalized sampling theorem to reconstruct undersampled non-Cartesian data.

Nicole Seiberlich1, Felix A Breuer, Philipp Ehses

  • 1Department of Radiology, University Hospitals of Cleveland, Cleveland, Ohio 44106, USA. nicole.seiberlich@case.edu

Magnetic Resonance in Medicine
|January 16, 2009
PubMed
Summary
This summary is machine-generated.

A new method called GROG-facilitated bunched phase encoding (GROG-BPE) uses self-calibrating GRAPPA operator gridding to acquire bunched data. This technique reduces scan time and image artifacts in undersampled magnetic resonance imaging (MRI) scans.

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Area of Science:

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

Background:

  • Generalized sampling theorem allows reduced scan time via bunched sampling and conjugate gradient (CG) reconstruction.
  • Acquiring bunched data typically requires modified pulse sequences and high gradient performance.

Purpose of the Study:

  • To introduce a novel method for generating bunched data using self-calibrating GRAPPA operator gridding (GROG).
  • To evaluate the effectiveness of GROG-facilitated bunched phase encoding (GROG-BPE) in reducing scan time and image artifacts.
  • To assess the impact of bunched point patterns, blip size, and quantity on reconstruction quality.

Main Methods:

  • Development of GROG-BPE, a parallel imaging technique that shifts k-space data points using the GRAPPA operator.
  • Utilizing CG reconstruction with additional bunched points to reconstruct images from undersampled data.
  • Performing simulations to analyze the influence of bunched point parameters on reconstruction quality.

Main Results:

  • GROG-BPE successfully generates bunched data without requiring modified pulse sequences or high gradient performance.
  • Reconstruction using GROG-BPE with CG significantly reduces artifacts in undersampled images.
  • Simulations provided insights into optimizing bunched point patterns for improved reconstruction.

Conclusions:

  • GROG-BPE offers a viable approach to decrease MRI scan time and improve image quality from undersampled data.
  • The method is compatible with various acquisition trajectories, including radial, spiral, and rosette.
  • This technique holds promise for enhancing MRI efficiency and diagnostic accuracy.