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 SNR            Signal to Noise Ratio 
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Signal to Noise Ratio
(SNR or S/N) The signal to noise ratio is used in MRI to describe the relative contributions to a detected signal of the true signal and random superimposed signals ('background noise') - a criterion for image quality.
One common method to increase the SNR is to average several measurements of the signal, on the expectation that random contributions will tend to cancel out. The SNR can also be improved by sampling larger volumes (increasing the field of view and slice thickness with a corresponding loss of spatial resolution) or, within limits, by increasing the strength of the magnetic field used. Surface coils can also be used to improve local signal intensity. The SNR will depend, in part, on the electrical properties of the sample or patient being studied. The SNR increases in proportion to voxel volume (1/resolution), the square root of the number of acquisitions (NEX), and the square root of the number of scans (phase encodings). SNR decreases with the field of view squared (FOV2) and wider bandwidths. See also Signal Intensity and Spin Density.
Measuring SNR:
Record the mean value of a small ROI placed in the most homogeneous area of tissue with high signal intensity (e.g. white matter in thalamus). Calculate the standard deviation for the largest possible ROI placed outside the object in the image background (avoid ghosting/aliasing or eye movement artifact regions).
The SNR is then:
Mean Signal/Standard Deviation of Background Noise
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Signal Averaging
A signal to noise improvement method that is accomplished by taking the average of several FID`s made under similar conditions to suppress the effects of random variations or random artifacts. It is a common method to increase the SNR by averaging several measurements of the signal.
The number of averages is also referred to as the number of excitations (NEX) or the number of acquisitions (NSA). Doubling the number of acquisitions will increase the SNR by the √2. The approximate amount of improvement in signal to noise (SNR) ratio is calculated as the square root of the number of excitations.
By using multiple averages, respiratory motion can be reduced in the same way that multiple averages increase the signal to noise ratio. NEX/NSA will increase SNR but will not affect contrast unless the tissues are being lost in noise (low CNR). Scan time scales directly with NEX/NSA and SNR as the square root of NEX/NSA.
The use of phase array coils allows the number of signal averages to be decreased with their superior SNR and resolution, thereby decreasing scan time.

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BandwidthForum -
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(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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Contrast to Noise Ratio
(CNR) In Magnetic Resonance Imaging MRI, Contrast to noise ratio is the relationship of signal intensity differences between two regions, scaled to image noise. Improving CNR increases perception of the distinct differences between two clinical areas of interest. A contrast to noise ratio is a summary of SNR and contrast. It is the difference in SNR between two relevant tissue types.
(A and B): CNR = SNRA - SNRB
See also Signal Intensity, Signal to Noise Ratio and Medical Imaging.

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3 Dimensional Imaging
A technique, which produces a 3 dimensional image of an object. The advantage of this approach is that the signal, acquired from the entire volume has an increased SNR. 'Slices' are defined by a second phase encoded axis, which divides the volume into 'partitions'. There is no gap between the slices in 3D volume imaging, therefore thin slices are possible. The Gz phase encoding gradient is set for several slices in one. But 3D takes more time with thin slices because of this phase encoding gradient. With conventional thin slice imaging, the SNR is poor, with 3D volume imaging this is not the case because the slab (volume) is responsible for SNR.
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