老师发的Correspondence - Beam-domain eigenspace-based minimum varian
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IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 60, . 12, DECEMBER 20132670
0885–3010/$25.00
©
2013 IEEE
Abstract—The eigenspace-based minimum variance (ES-
BMV) beamformer can provide good imaging resolution and
contrast; however, the performance is achieved at the cost of
high computational complexity. In adaptive array processing,
the beamspace method is an efficient way to lower the compu-
tational complexity. In this paper, we combine the beamspace
method with the ESBMV beamformer and propose a beam-
domain ESBMV beamformer. We demonstrate the feasibility
of introducing the beamspace into the ESBMV beamformer
and propose an effective method of forming the transform ma-
trix based on the spatial spectrum of the array signals. We
also illustrate the performance of the proposed beamformer
when resolving point scatterers and a cyst phantom with both
simulated and experimental data. The results show that the
proposed method can achieve performance comparable to the
ESBMV beamformer within much shorter time.
I. I
I
medical ultrasound imaging, beamforming is con-
ventionally carried out by the delay-and-sum (DAS)
method. Because it uses predefined and data-independent
weights, the DAS beamformer is weak in suppressing in-
terference and noise, resulting in relatively poor imaging
resolution and contrast. To improve the imaging resolu-
tion, adaptive beamformers were introduced into medical
ultrasound imaging. Among these adaptive beamformers,
the minimum variance (MV) beamformer, originally intro-
duced by Capon in 1969 [1], is a widely used method. The
weights of the MV beamformer are calculated by minimiz-
ing the power of the beamformer output subject to the
constraint that the response from the focus point is passed
without distortion. Several researchers have investigated
the MV beamformer during the past decades. Mann [2]
proposed the Frost beamformer. Sasso and Cohen-Bacire
[3] introduced the spatial smoothing technique to obtain
a well-conditioned covariance matrix. Synnevåg et al. ap-
plied the diagonal loading [4] technique in the estimation
of the covariance matrix to ensure its robustness. Holfort
et al. implemented the MV beamformer in the frequency
domain and proposed the broad-MV beamformer [5]. In
addition, coherence-factor methods have also been inves-
tigated to improve the performance of MV beamformer
[6], [7].
Previous works have shown that the MV beamform-
er offers a better resolution than the DAS beamformer.
However, the improvement for imaging contrast is not as
significant as for resolution [8]. Hence, eigenspace-based
methods have been proposed. These methods utilize the
orthogonal property of the signal and the noise subspace
constructed by the eigenvectors of the covariance matrix
[9]. The signal subspace represents the information of the
main lobe signals, whereas the noise subspace is related
to the side lobe signals. In the eigenspace-based minimum
variance (ESBMV) beamformer proposed by Asl and
Mahloojifar [8], the weights are optimized by projecting
the MV weights onto the constructed signal subspace. In
this way, the contribution of the side lobe signals can be
greatly reduced, but the contribution of the main lobe
signals remains, which leads to a significant improvement
in imaging resolution and contrast [10], [11].
However, the eigen-decomposition of the covariance
matrix adds many calculations. Although the computa-
tional overheads brought by the eigen-decomposition and
inversion of the covariance matrix are both cubic with
the array size, O(L
3
), the coefficient before the cubic term
is much bigger in eigen-decomposition than in inversion.
Therefore, it is necessary to lower the computational com-
plexity of the ESBMV beamformer.
The study of the low-complexity adaptive beamformer
has been an area of great interest in ultrasound imaging.
Several methods have been proposed. A direct method
is reducing the number of array elements used to emit
or receive the echo waves, such as the method proposed
by Vignon and Burcher [12]. However, this method either
affects the imaging resolution or makes the beamformer
susceptible to signal cancellation because of lack of spatial
smoothing. Another low-complexity beamformer was pro-
posed by Synnevåg et al. [13]. In this method, the weights
of the beamformer leading to the lowest output power are
selected from a predefined set of distortionless weights.
However, because the best weights may be different for
different scenarios, the performance of this method de-
pends very much on the window design [13]. In [14], Asl
and Mahloojifar applied the Toeplitz structure into esti-
mating the covariance matrix. The computational loads
can be reduced from O(L
3
) to O(L
2
) using the fast algo-
rithm for the inversion of the Toeplitz matrix.
Because the calculation of the ESBMV weights involves
not only the inversion but also the eigen-decomposition of
the covariance matrix, the improvement brought by the
Beam-Domain Eigenspace-Based
Minimum Variance Beamformer
for Medical Ultrasound Imaging
Xing Zeng, Yuanyuan Wang, Senior Member, IEEE,
Jinhua Yu, and Yi Guo
Correspondence
Manuscript received April 25, 2013; accepted September 12, 2013.
This work is supported by the National Natural Science Foundation of
China (grant numbers 61271071 and 11228411), the National Key Tech-
nology R&D Program of China (grant number 2012BAI13B02), and the
Specialized Research Fund for the Doctoral Program of Higher Educa-
tion of China (grant number 20110071110017).
The authors are with the Department of Electronic Engineering, Fu-
dan University, Shanghai, China (e-mail: [email protected]).
DOI http://dx.doi.org/10.1109/TUFFC.2013.2866
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