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Related Concept Videos

Convolution Properties II01:17

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
Convolution Properties I01:20

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
Deconvolution01:20

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
Reducing Line Loss01:18

Reducing Line Loss

In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss in...
Masking and Demasking Agents01:19

Masking and Demasking Agents

EDTA titrations may necessitate masking and demasking agents to temporarily protect a particular metal ion in a mixture from the EDTA reaction. These agents facilitate the sequential analysis of the metal ions by forming stable complexes with some—but not all—metal ions during certain steps.
There are many masking agents, such as cyanide, fluoride, triethanolamine, thiourea, and 2,3-bis(sulfanyl)propan-1-ol (formerly 2,3-dimercapto-1-propanol), with the masking agent chosen based on the metal...

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Related Experiment Videos

Data convolution and combination operation (COCOA) for motion ghost artifacts reduction.

Feng Huang1, Wei Lin, Peter Börnert

  • 1Invivo Corporation, Gainesville, Florida 32608, USA. fhuang@invivocorp.com

Magnetic Resonance in Medicine
|June 24, 2010
PubMed
Summary

A new convolution method effectively reduces motion artifacts in medical imaging. This technique minimizes ghosting caused by breathing or blood flow, improving image quality with minimal signal loss.

Related Experiment Videos

Area of Science:

  • Medical Imaging
  • Signal Processing
  • Magnetic Resonance Imaging (MRI)

Background:

  • Motion and flow artifacts significantly degrade image quality in MRI.
  • Existing artifact reduction methods often have limitations or impact image signal-to-noise ratio.

Purpose of the Study:

  • To introduce a novel, self-calibrated method for reducing motion and flow artifacts in k-space data.
  • To demonstrate the effectiveness of the proposed method in eliminating or reducing ghost artifacts.

Main Methods:

  • A novel data convolution and combination operation is proposed.
  • Synthetic k-space data with dispersed artifacts are generated via convolution for each coil.
  • Convolution kernels are self-calibrated using acquired k-space data.
  • Consistency checks between synthetic and acquired data identify motion-corrupted regions.
  • Appropriate combination of data sets reduces motion-induced errors.

Main Results:

  • The method effectively reduces ghost artifacts caused by swallowing, breathing, and blood flow.
  • Isolated errors in k-space can be completely eliminated.
  • Widespread errors are significantly reduced.
  • Minimum impact on image signal-to-noise ratio is observed.
  • Robust performance demonstrated with simulated and in vivo data.

Conclusions:

  • The proposed data convolution and combination method offers robust artifact reduction in MRI.
  • This self-calibrated approach improves image quality by minimizing ghosting.
  • The technique is effective for various motion sources without substantial SNR degradation.