Biomedical Engineering Reference
In-Depth Information
regularization methods include filtered backprojection (FBP) with nonlinear
filtering corrections, expectation-maximization and maximum
a posteriori
esti-
mators [63-66]. The most commonly used tomographic reconstruction method
combines a low-pass filter, for noise suppression, and a ramp filter for standard
filtered backprojection algorithm. The cut-off frequency of the low-pass filter
controls the balance between SNR and spatial resolution. While high-frequency
noise is eliminated after low-pass filtering, useful high-frequency information,
such as sharp varied signals and edges, is also attenuated. In addition, noise com-
ponents in low-frequency bands still exist. For these two reasons, tomographic
images reconstructed with FBP algorithms often suffer from over-smoothness
or/and low SNR. Post-processing including denoising and enhancement is there-
fore helpful in improving image qualities for reliable clinical interpretation.
As low-pass filtering has always been considered one of the most fundamen-
tal denoising techniques, embedding a multiscale denoising module to partially
replace the low-pass filtering operator in the FBP algorithm can potentially im-
prove the image quality of reconstruction in terms of both spatial resolution and
signal-to-noise ratio. The intuitive approach to combine FBP and denoising is
therefore to preserve more high-frequency features during the FBP reconstruc-
tion by using a low-pass filter with higher cut-off frequency, or removing the low-
pass prefiltering. The noise mixed with the high-frequency signal components is
then further processed via a multiscale denoising operator. An illustration of the
denoising performance is provided in Fig. 6.19 for simple comparison between
traditional FBP using a clinical console (low-pass filter using Hann filter with cut-
off frequency set to 0.4) and the proposed two-step processing. It can be observed
that the second method, based on FBP using Hann filter with a higher cut-off
frequency, generates a reconstructed image containing more detailed informa-
tion as well as more significant noisy features. After multiscale denoising (com-
bining wavelet packets thresholding and brushlet thresholding), image quality
markedly improved, showing more anatomical details and spatial information.
Thresholding on Three-Dimensional Wavelet Modulus.
Both PET and
SPECT image reconstructed using FBP display strong directional noise pat-
terns. Most feature-based denoising methods, including wavelet thresholding,
are based on edge information and are not suited to directional noise compo-
nents that resemble strong edges. Indeed, edge information alone cannot accu-
rately separate noise from meaningful signal features in a single image. A novel
approach to overcome this limitation is to apply the multiscale analysis and
