A novel adaptive beamformer named filtered-delay multiply and sum (F-DMAS) has recently been proposed. Compared to the delay and sum (DAS) beamforming algorithm, F-DMAS can efficiently improve the resolution and contrast. However, the DAS can still be seen in the expansion of DMAS. Therefore, we rearrange the pair-wised signals in terms of lag in DMAS and then synthesize a lot of new signals. Thanks to the relationship between the spatial coherence and lag, these new signals can be thought of as sorted by the spatial coherence. Thus, we apply two phase-related factors, the polarity-based factor (PF) and the sign coherence factor (SCF), which are evaluated based on new signals, to weight the output of DMAS. The two approaches are consequently referred to as LAG-DMAS-PF and LAG-DMAS-SCF, respectively. The results show that, compared to F-DMAS and DAS, our proposed methods can improve the resolution and contrast to some extent without increasing too much computational complexity. In the comparison between LAG-DMAS-PF and LAG-DMAS-SCF, the latter has better performance, but the former can better protect image details.
Ultrasound imaging technology has been widely used for decades. The beamformer, as an important component in ultrasound imaging system, has made great progress and evolved from analog technology to digital technology [
In addition to the methods we mentioned previously, a novel filtered-delay multiply and sum (F-DMAS) beamformer has been proposed for ultrasound B-mode medical imaging [
The F-DMAS beamforming algorithm exploits the spatial coherence to enhance the image quality. In fact, there are many other ways to use the coherence besides the F-DMAS. One of them is to use the sign coherence factor (SCF) proposed by Camacho et al. [
In SCF, The received signals are divided into two polarities, positive and negative, according to different phases. SCF is calculated based on the statistical characteristic (standard deviation) of polarities. Then, the SCF is applied to weight the output of the DAS beamformer. However, because the polarity reflects the phase of the signal, one can also use a mean value of signals' polarities as a factor which we refer to as polarity-based factor (PF). Based on the F-DMAS and SCF, we proposed two new methods, the lag-based delay multiply and sum weighted by SCF (LAG-DMAS-SCF) and the lag-based delay multiply and sum weighted by PF (LAG-DMAS-PF). First, we construct a series of new signals based on the lag. The SCF and PF are then calculated from the new generated signals. Finally, the two factors are separately applied to weight the output of the DMAS beamformer.
The rest paper is organized as follows. Section
The algebra of DMAS algorithm is written as
Substituting Equation (
The SCF is an extreme form of PCF which utilizes the phases of received signals to evaluate the signal coherence [
The DMAS algebra can be expanded to
Each item in Equation (
The DMAS can then be re-written as
Here,
Let the SCF of the
Multiplying the
Considering that the computational complex of SCF is somewhat high, we proposed another polarity-based factor (PF):
This factor is actually an average value of all polarities. It can also reflect the phase diversity to a certain extent. Multiplying this factor with DMAS, we can get the final result
The performance of four beamformers, DAS, F-DMAS, LAG-DMAS-PF, and LAG-DMAS-SCF, is compared. The software Field II [
In the simulation tests, a linear array with 128 elements and 38.4 mm width is modeled. In addition, the element width is 0.27 mm, element height is 5 mm, pitch size is 0.3 mm, and kerf is 0.03 mm. The elevation focus is at 30 mm. Two cycles of Hanning weighted sinusoidal excitation pulse is modeled, and the center frequency is 5 MHz. The sample frequency is 120 MHz. A low-pass filter is employed to remove the undesirable frequency components in the beamformed signals [
Twelve points are synthesized in the depth range from 15 mm to 40 mm with a 5 mm step, and there are 2 points at each depth. The lateral coordinates of two points at each depth are
The reconstructed images by DAS, F-DMAS, LAG-DMAS-PF, and LAG-DMAS-SCF are shown in Figure
Images of simulated point targets reconstructed by (a) DAS, (b) F-DMAS, (c) LAG-DMAS-PF, and (d) LAG-DMAS-SCF. All images are shown in a dynamic range of 60 dB.
Figure
Lateral cross-sections in Figure
FWHM (mm) at different depths in Figure
Depth (mm) | Beamformer | |||
---|---|---|---|---|
DAS | F-DMAS | LAG-DMAS-PF | LAG-DMAS-SCF | |
15 | 0.48 | 0.32 | 0.22 | |
20 | 0.55 | 0.36 | 0.31 | |
25 | 0.50 | 0.35 | 0.31 | |
30 | 0.67 | 0.41 | 0.36 | |
35 | 0.80 | 0.53 | 0.38 | |
40 | 0.91 | 0.67 | 0.49 |
In the point target simulation, we can observe that applying a phase-related factor to weight the DMAS can get a better result. In the comparison between LAG-DMAS-PF and LAG-DMAS-SCF, the performance of LAG-DMAS-SCF is better.
A simulated anechoic cyst phantom is synthesized to evaluate the contrast of the images reconstructed by four algorithms. In a
Figures
Images of simulated cyst reconstructed by (a) DAS, (b) F-DMAS, (c) LAG-DMAS-PF, and (d) LAG-DMAS-SCF. All images are shown in a dynamic range of 70 dB.
Lateral cross-section in Figure
The contrast ratio (CR) which is normally used to quantitatively estimate the contrast is calculated by [
Noise is a very important factor affecting the quality of ultrasound images. Therefore, we try to evaluate the effects of the noise on the four algorithms. White Gaussian noise with SNR 10 dB is then added into the previous simulated point targets. The reconstructed images are shown in Figure
Images of simulated point targets with white Gaussian noise (
In Figures
Lateral cross-sections in Figure
FWHM (mm) at different depths in Figure
Depth(mm) | Beamformer | |||
---|---|---|---|---|
DAS | F-DMAS | LAG-DMAS-PF | LAG-DMAS-SCF | |
15 | 0.47 | 0.32 | 0.23 | |
20 | 0.55 | 0.36 | 0.32 | |
25 | 0.52 | 0.35 | 0.32 | |
30 | 0.66 | 0.40 | 0.36 | |
35 | 0.79 | 0.52 | 0.38 | |
40 | 0.90 | 0.63 | 0.51 |
In some cases, the contrast of target with respect to background may be not very high. The target is hard to detect accordingly. To evaluate the performance of four algorithms in these cases, we used a medical ultrasound machine iNSIGHT 37C (Saset, Chengdu, China) to get RF data by scanning a Multipurpose Multitissue ultrasound phantom (Model 040GSE. CIRS INC. 900 Asbury Ave Norfolk, Virginia 23513 USA). The center frequency and sampling frequency are 10 MHz and 60 MHz, respectively. The number of scan lines is 302. According to the phantom specification, the diameters of two gray scale targets, whose contrasts with respect to background are -9 dB and -6 dB, respectively, are both 8 mm.
The reconstructed images by the four beamformers are illustrated in Figure
Images of a tissue phantom reconstructed by (a) DAS, (b) F-DMAS, (c) LAG-DMAS-PF, and (d) LAG-DMAS-SCF. All images are shown in a dynamic range of 60 dB.
The corresponding values of CR evaluated using Equation (
CRs (dB) of two gray scale targets in Figure
Gray scale target | Beamformer | |||
---|---|---|---|---|
DAS | F-DMAS | LAG-DMAS-PF | LAG-DMAS-SCF | |
Left | -8.72 | -7.94 | -13.75 | |
Right | -12.36 | -11.30 | -21.02 |
We also used the same ultrasound machine to scan the carotid artery. The number of scan lines is also 302. The reconstructed images are shown in Figure
Images of a carotid artery reconstructed by (a) DAS, (b) F-DMAS, (c) LAG-DMAS-PF, and (d) LAG-DMAS-SCF. All images are shown in a dynamic range of 60 dB.
In the DMAS beamforming algorithm, the signals are multiplied in pairs and then summed. If there are
In our proposed methods, two factors, SCF and PF, are selected. As introduced earlier, the SCF and PF are both based on the polarity (or phase) of each signal; in our case, it is the polarity of each new synthesized signal. The spatial coherence is proportional to the autocorrelation of aperture function [
The results show that the LAG-DMAS-PF and LAG-DMAS-SCF, in terms of resolution and contrast, outperform the DAS and F-DMAS. For a comparison between LAG-DMAS-PF and LAG-DMAS-SCF, the latter is better. However, compared to LAG-DMAS-PF, the dark hole phenomenon is more severe in LAG-DMAS-SCF. This may lead to the weakness of tissue structure. Therefore, if one wants to maintain the tissue structure as much as possible and hopes that the target can be better detected, the LAG-DMAS-PF is a good choice.
Compared to the original DMAS algorithm, there is only one more step to calculate the PF and SCF in LAG-DMAS-PF and LAG-DMAS-SCF, respectively. The computational complexity of SCF may be slightly high; however, the calculation of PF is really simple. Therefore, this point can also be used as a basis for choosing LAG-DMAS-PF or LAG-DMAS-SCF.
In this paper, we have presented two methods to improve the performance of the F-DMAS beamformer. The F-DMAS algorithm exploits the spatial coherence to enlarge the difference between the correlated signals and uncorrelated signals. Thus, we apply two phase coherence-related factors, which can also effectively reflect the spatial coherence, to enhance this feature. The results show that our proposed algorithms can improve the resolution and contrast to a certain extent.
All data generated or analyzed during this study are included in this published article.
The authors declare that there are no potential conflicts of interest in the research, authorship, and/or publication of this article.
We would like to appreciate the support from Saset (Chengdu) Inc. This work was supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201801606), the Natural Science Foundation Project of CQ CSTC (cstc2017jcyjAX0092), the Chongqing Big Data Engineering Laboratory for Children, the Chongqing Electronics Engineering Technology Research Center for Interactive Learning, and the Scientific Research Program of Chongqing University of Education (KY201924C).