Dynamic Range Requirements for MRI
RAYHAN BEHIN,
1
JONATHAN BISHOP,
1
R. MARK HENKELMAN
1,2
1
Mouse Imaging Centre (MICe), The Hospital for Sick Children, 555 University Avenue,Toronto,
Ontario M5G 1X8, Canada
2
Department of Medical Biophysics,University of Toronto,Toronto,Canada
ABSTRACT: In order to realize the full potential in an MR receiver, the digitizer must
capture a signal magnitude range from the central k-space peak to the thermal noise floor
of the system. This dynamic range can exceed the performance of standard 16-bit data
converters. For example, a whole-body mouse scan in a 7 Tesla magnet requires 20 bits of
dynamic range. A 3D high-resolution mouse scan at 75 m isotropic voxel resolution using
a 16-bit spectrometer shows an eightfold improvement in image SNR by gain stepping the
receiver prior to digitization to cover the full magnitude dynamic range compared to a
standard fixed gain approach. A method is presented to determine the dynamic range
requirements of any experiment. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part B
(Magn Reson Engineering) 26B: 28 –35, 2005
KEY WORDS: MRI; high resolution; dynamic range; analog to digital; quantization noise;
thermal noise; variable gain; signal-to-noise ratio (SNR); k-space sampling
INTRODUCTION
The frequency space (k-space) domain of magnetic
resonance (MR) imaging is highly peaked at the cen-
ter (low spatial frequencies) and falls off rapidly to-
ward the periphery of k-space. Accurate digitization
of this space requires representation at the central
point and at the thermal noise level of the system.
This range in signal intensity is typically referred to as
the dynamic range (DR). High-resolution 3D imaging
pushes the dynamic range requirements, ultimately to
the thermal noise level of the receiver.
Magnetic resonance (MR) imaging systems typi-
cally use a quadrature pair of 16-bit analog-to-digital
converters (ADC) operating at 1 MSps (megasamples
per second). With low noise receivers and higher
magnetic fields, these systems may be signal-to-noise
ratio (SNR) limited by the bit resolution of the ADC.
This article illustrates through experiment the lin-
ear relationship between k-space log magnitude and
log radius for a natural image. This relationship is
used to determine the range in k-space signal magni-
tude for a given sample volume at any imaging reso-
lution. Finally, a method is given to determine the
dynamic range requirements for any MR setup.
THEORY
k-Space
MR imaging involves the capture of complex data in
spatial frequency (k-space). This data is usually trans-
formed by means of a Fourier transform to represent the
magnitude image intensity as a function of spatial posi-
tion—in other words, an image in real space. The units
of measure in k-space is inverse distance (m
-1
) and in
the transformed real space image is distance (m). The
extent of k-space coverage in each frequency axis is
inversely proportional to the pixel size in real image
space along the corresponding axis. The separation of
k-space samples in each frequency axis is inversely
Received 23 November 2004; accepted 14 February
2005
Correspondence to: Rayhan Behin; E-mail: rbehin@sickkids.ca
Concepts in Magnetic Resonance Part B (Magnetic Resonance
Engineering), Vol. 26B(1) 28 –35 (2005)
Published online in Wiley InterScience (www.interscience.wiley.
com). DOI 10.1002/cmr.b.20042
© 2005 Wiley Periodicals, Inc.
28