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Related Concept Videos

Properties of DTFT I01:24

Properties of DTFT I

In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
Difference from Background: Limit of Detection01:05

Difference from Background: Limit of Detection

The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the concentration at which the analyte signal is three times larger than the standard deviation of the blank signal. Below this value, the analyte signal cannot be differentiated from the background noise. It is calculated by dividing the calibration slope by 3 times the standard deviation of the blank signals.
The LOD indicates the presence or absence...
Properties of DTFT II01:24

Properties of DTFT II

In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω. Multiplying by j...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)01:20

¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)

When proton-coupled carbon-13 spectra are simplified by a broadband proton decoupling technique, structural information about the coupled protons is lost. Distortionless enhancement by polarization transfer (DEPT) is a technique that provides information on the number of hydrogens attached to each carbon in a molecule. While the DEPT experiment utilizes complex pulse sequences, the pulse delay and flip angle are specifically manipulated. The resulting signals have different phases depending on...
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...

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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

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Published on: July 28, 2013

How background noise shifts eigenvectors and increases eigenvalues in DTI.

Frederik Bernd Laun1, Lothar Rudi Schad, Jan Klein

  • 1Medical Physics in Radiology, German Cancer Research Center, Heidelberg, Germany. f.laun@dkfz.de

Magma (New York, N.Y.)
|December 11, 2008
PubMed
Summary
This summary is machine-generated.

Two new artifacts in diffusion tensor imaging (DTI) can significantly impact results when signal-to-noise ratios are low. These findings are crucial for understanding DTI data in clinical settings.

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Area of Science:

  • Medical Imaging
  • Neuroimaging
  • Biophysics

Background:

  • In vivo diffusion tensor imaging (DTI) often suffers from limited signal-to-noise ratio (SNR), particularly with high-resolution data acquisition.
  • Low SNR can cause diffusion-weighted image signals to fall below background noise, leading to underestimated diffusion constants.
  • This study identifies and characterizes two novel artifacts in DTI relevant to low SNR conditions.

Purpose of the Study:

  • To report and describe two previously unrecognized artifacts in diffusion tensor imaging (DTI).
  • To analyze the impact of these artifacts on DTI data quality and interpretation.
  • To assess the clinical relevance of these artifacts in current DTI applications.

Main Methods:

  • Analytical and numerical descriptions of the identified artifacts.
  • Experimental validation using DTI phantoms.
  • In vivo demonstration of artifacts in human subjects.

Main Results:

  • Systematic shifts in eigenvectors towards specific gradient scheme orientations were observed.
  • Overestimation of certain eigenvalues due to underestimated diffusion, potentially causing eigenvalue misordering.
  • Demonstration of these artifacts in both phantom and in vivo DTI data.

Conclusions:

  • The identified artifacts significantly affect DTI data quality, especially under low SNR conditions.
  • These artifacts have direct implications for the interpretation of DTI metrics in clinical practice.
  • Understanding these artifacts is essential for accurate DTI analysis in neuroimaging and other applications.