Image Processing Reference
In-Depth Information
additional time averages (higher number of excitations [NEX]) and, consequently,
a longer acquisition time. But a long acquisition time is undesirable because of
constraints such as patient comfort, system throughput, and physical limitations
arising in dynamic applications such as cardiac imaging and functional MRI. In
such cases, time averaging is replaced by spatial averaging.
Spatial filtering of MR image data should ideally be fulfilled by removing
the noise without loss of resolution, improving the image contrast, to obtain
piecewise constant or slowly varying signals in homogeneous tissue regions,
minimizing information loss by preserving detailed structures inside objects and
object boundaries. Spatial filtering techniques are applied under two important
assumptions: (a) the image is supposed to consist of many regions in which the
signal is stationary and ergodic in the mean and variance [2] and (b) the image
noise is assumed to be zero mean and Gaussian distributed. The main problem
is to find these stationary regions.
The problem of finding the proper stationary area for local signal estimation is
partly solved by choosing filters that are able to distinguish homogeneous regions
from those with edge regions. In the literature, many approaches to improve SNR,
CNR and edge blurring effects have been proposed, such as adaptive filters [3-5],
wavelet filters [6-11], and anisotropic diffusion filters [12-17].
In particular, anisotropic diffusion [12] is an accepted filtering technique that
is well suited for practical use because of its computational speed and algorithmic
simplicity. The filter assumes image noise to be Gaussian distributed. The aniso-
tropic diffusion filter has proved to be particularly effective in prefiltering of MR
images before the automatic image segmentation procedure [16,18] and before
MRI inhomogeneity correction [19]. Subsequently, the standard anisotropic dif-
fusion method was extended by Yang [20] using both a local intensity orientation
and an anisotropic measure of level contours, instead of utilizing local gradients
to control the anisotropism of the filters.
When processing magnitude MR data, a Gaussian assumption for image noise
is not acceptable as it can be shown to be Rice distributed, especially in regions
with low SNR [3,21-23].
Not incorporating this knowledge leads inevitably to biased results, in par-
ticular, when applying such filters in regions with low SNR. In order to reduce
this bias, Sijbers et al. [24] proposed a modified version of the anisotropic filter
suggested by Yang
[20], in which the Rician nature of the data is exploited.
Wavelet-based methods that explicitly account for the Rician nature of the data
are described in [25-27].
How noise is spatially distributed is another issue concerning MR image noise
that should be considered before applying noise filters. Examples include images
multiplicatively corrected for intensity inhomogeneity [19,28], and particularly,
images obtained with partially parallel imaging techniques [29-35]. Retrospective
denoising with a nonlinear technique such as anisotropic diffusion filtering has
been demonstrated to be an attractive option for improving the SNR of partially
parallel images [36]. Topics dealing with noise in parallel MRI will be discussed
in this topic in another chapter.
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