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Aliasing
 
If the receiving RF coil is sensitive to tissue signal arising from outside the desired FOV, this undesired signal may be incorrectly mapped to a location within the image, a phenomenon known as aliasing. This is a consequence of the acquired k-space frequencies not being sampled densely enough, whereby portions of the object outside of the desired FOV get mapped to an incorrect location inside the FOV. The sampling frequency should be at least twice the frequency being sampled. The maximum measurable frequency is therefore equal to half the sampling frequency. This is the so-called Nyquist limit. When the frequency is higher than the Nyquist limit, aliasing occurs.
A similar problem occurs in the phase encoding direction, where the phases of signal-bearing tissues outside of the FOV in the y-direction are a replication of the phases that are encoded within the FOV. This signal will be mapped, or wrapped back into the image at incorrect locations, and is seen as artifact.
See also Aliasing Artifact.

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    • Nyquist Limit
    • Oversampling
    • Foldover Suppression
    • Phase Encoding
    • Aliasing Artifact
 
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The Effects of Breathing Motion on DCE-MRI Images: Phantom Studies Simulating Respiratory Motion to Compare CAIPIRINHA-VIBE, Radial-VIBE, and Conventional VIBE
Tuesday, 7 February 2017   by www.kjronline.org    
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Anti Aliasing
 
Anti aliasing is a method to prevent aliasing artifacts by properly choosing the sampling rate. The signal is sampled at a higher bandwidth than required.
See Oversampling.
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Aliasing ArtifactInfoSheet: - Artifacts - 
Case Studies, 
Reduction Index, 
etc.MRI Resource Directory:
 - Artifacts -
 
Quick Overview
Please note that there are different common names for this MRI artifact.

Artifact Information
NAME Aliasing, backfolding, foldover, phase wrapping, wrap around
DESCRIPTION Image wrap around
REASON Undersampling in k-space
HELP Larger FOV, oversampling, foldover suppression

Aliasing is an artifact that occurs in MR images when the scanned body part is larger than field of view (FOV). As a consequence of the acquired k-space frequencies not being sampled densely enough, whereby portions of the object outside of the desired FOV get mapped to an incorrect location inside the FOV. The cyclical property of the Fourier transform fills the missing data of the right side with data from behind the FOV of the left side and vice versa. This is caused by a too small number of samples acquired in, e.g. the frequency encoding direction, therefore the spectrums will overlap, resulting in a replication of the object in the x direction.
Aliasing in the frequency direction can be eliminated by twice as fast sampling of the signal or by applying frequency specific filters to the received signal.
A similar problem occurs in the phase encoding direction, where the phases of signal-bearing tissues outside of the FOV in the y-direction are a replication of the phases that are encoded within the FOV. Phase encoding gradients are scaled for the field of view only, therefore tissues outside the FOV do not get properly phase encoded relative to their actual position and 'wraps' into the opposite side of the image.


Image Guidance
Use a larger FOV, RFOV or 3D Volume, apply presaturation pulses to the undesired tissue, adjust the position of the FOV, or select a small coil which will only receive signal from objects inside or near the coil. The number of phase encoding steps must be increased in phase direction, unfortunately resulting in longer scan times.
When this is not possible it can be corrected by oversampling the data. Aliasing is eliminated by Oversampling in frequency direction. No Phase Wrap (Foldover Suppression) options typically correct the phase encoding by doubling the field of view, doubling the number of phase encodes (to keep resolution constant) and halving the number of averages (to keep scan time constant) then discarding the additional data and processing the image within the desired field of view (but this is more time consuming).
Tissue outside this doubled area can be folded nevertheless into the image as phase wrap. In this case combine more than 2 number of excitations / number of signal averages with foldover suppression.
See also Aliasing, Foldover Suppression, Oversampling, and Artifact Reduction - Aliasing.

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Oversampling
 
Oversampling is the increase in data to avoid aliasing and wrap around artifacts. Aliasing is the incorrectly mapping of tissue signal from outside the FOV to a location inside the FOV. This is caused by the fact, that the acquired k-space frequency data is not sampled density enough.
Oversampling in frequency direction, done by increasing the sampling frequency, prevents this aliasing artifact. The proper frequency based on the sampling theorem (Shannon sampling theorem/Nyquist sampling theorem) must be at least twice the frequency of each frequency component in the incoming signal. All frequency components above this limit will be aliased to frequencies between zero and half of the sampling frequency and combined with the proper signal information, which creates the artifact. Oversampling creates a larger field of view, more data needs to be stored and processed, but this is for modern MRI systems not a real problem. Oversampling in phase direction (no phase wrap), to eliminate wrap around artifacts, by increasing the number of phase encoding steps, results in longer scan/processing times.
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Further Reading:
  Basics:
The Basics of MRI
   by www.cis.rit.edu    
The Scientist and Engineer's Guide to Digital Signal Processing
   by www.dspguide.com    
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BandwidthForum -
related threads
 
(BW) Bandwidth is a measure of frequency range, the range between the highest and lowest frequency allowed in the signal. For analog signals, which can be mathematically viewed as a function of time, bandwidth is the width, measured in Hertz of a frequency range in which the signal's Fourier transform is nonzero.
The receiver (or acquisition) bandwidth (rBW) is the range of frequencies accepted by the receiver to sample the MR signal. The receiver bandwidth is changeable (see also acronyms for 'bandwidth' from different manufacturers) and has a direct relationship to the signal to noise ratio (SNR) (SNR = 1/squareroot (rBW). The bandwidth depends on the readout (or frequency encoding) gradient strength and the data sampling rate (or dwell time).
Bandwidth is defined by BW = Sampling Rate/Number of Samples.
A smaller bandwidth improves SNR, but can cause spatial distortions, also increases the chemical shift. A larger bandwidth reduces SNR (more noise from the outskirts of the spectrum), but allows faster imaging.
The transmit bandwidth refers to the RF excitation pulse required for slice selection in a pulse sequence. The slice thickness is proportional to the bandwidth of the RF pulse (and inversely proportional to the applied gradient strength). Lowering the pulse bandwidth can reduce the slice thickness.



Image Guidance
A higher bandwidth is used for the reduction of chemical shift artifacts (lower bandwidth - more chemical shift - longer dwell time - but better signal to noise ratio). Narrow receive bandwidths accentuate this water fat shift by assigning a smaller number of frequencies across the MRI image. This effect is much more significant on higher field strengths. At 1.5 T, fat and water precess 220 Hz apart, which results in a higher shift than in Low Field MRI.
Lower bandwidth (measured in Hz) = higher water fat shift (measured in pixel shift).
See also Aliasing, Aliasing Artifact, Frequency Encoding, and Chemical Shift Artifact.

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Further Reading:
  Basics:
Bandwidth
   by en.wikipedia.org    
  News & More:
Automated Quality Assurance for Magnetic Resonance Image with Extensions to Diffusion Tensor Imaging(.pdf)
   by scholar.lib.vt.edu    
A Real-Time Navigator Approach to Compensating for Motion Artifacts in Coronary Magnetic Resonance Angiography
   by www.cs.nyu.edu    
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