Biomedical Engineering Reference
In-Depth Information
and statistical methods adapted respectively to macro- and micro-textural ele-
ments. Recent work on texture characterization and more specifically denoising
of ultrasound data via spatio-temporal analysis include steerable filters and Ga-
bor oriented filters [61, 62]. Both techniques are nonorthogonal and therefore
suffer from noncomplete partitioning of the Fourier domain. As we showed
in previous section, brushlets allow more flexibility on the partitioning of the
Fourier domain and work with an orthogonal basis that provides perfect re-
construction of an original signal. In this application, modifications from the
original implementation, which extended the analysis to three and four dimen-
sions and performed the analysis in an overcomplete framework, have been
made.
Brushlet basis functions decompose an
N
-dimensional signal along specific
spatial-directions via analysis of its Fourier domain. As they only depend on
spatial-frequency content, brushlet decompositions are invariant to the inten-
sity or contrast range in the original data. This makes them very suitable and
a powerful basis for the analysis of RT3D ultrasound where choosing a single
global-intensity-based edge threshold is not possible due to position-dependent
attenuation of the signal. There are as many basis functions as there are subin-
tervals in the Fourier domain defining brushstrokes associated with the center
frequency of each interval. The tiling of the Fourier domain therefore determines
the resolution and orientation of the brushlet basis functions as illustrated in
Fig. 6.12(a).
The resolution of each brushstroke is inversely proportional to the size of
the interval, as illustrated in Fig. 6.12(b). The major difference between the
brushlet basis and wavelet packets is the possibility of any arbitrary tiling of the
time-frequency plane and the perfect localization of a single frequency in one
coefficient.
Spatial Denoising via Thresholding.
Denoising was performed via thresh-
olding of the brushlet coefficients. In the case of RT3D ultrasound, speckle noise
components are concentrated in the high-frequency coefficients without specific
direction whereas cardiac structures are decomposed into the low-frequency
components along different orientations. Decorrelation of signal and noise in the
frequency domain was therefore performed by removing the higher frequency
components and thresholding only the lower frequency components prior to
reconstruction. Denoising performance was compared for processing in 2D and
