Far-focus compound ultrasound imaging with lag-one coherence-based zero-cross factor

Abstract

BACKGROUND:

OBJECTIVE:

Improving image quality of SA-based methods using an improved imaging mode named far-focus compound (FSC) imaging.

METHODS:

A far-focus compound (FSC) imaging based on full-aperture transmission and full-aperture reception is proposed in this paper. In transmission, it uses the full aperture to transmit the focused beam to ensure image resolution and emission of sound field energy. In reception, the full aperture is used to receive the reflected beam to ensure the image quality. A lag-one coherence-based zero-cross factor (LOCZF) is then implemented in FSC for improvement of contrast ratio (CR). The LOCZF uses lag-one coherence as zero-cross factorâ€™s adaptive coefficient. Comparisons were made with several other weighting techniques by performing simulations and experiments for performance evaluation.

RESULTS:

Results confirm that LOCZF applied to FSC offers a good image contrast and simultaneously the speckle pattern. For simulated cysts, CR improvement of LOCZF reaches 194.1%. For experimental cysts, CR improvement of LOCZF reaches 220%. From the in-vivo result, compared with FSC, CR improvement of LOCZF reaches 112.7%.

CONCLUSION:

Proved gCNR performance. In addition, the LOCZF method shows good performance in experiments. The proposed method can be used as an effective weighting technique for improvement of image quality in ultrasound imaging.

Keywords

Ultrasonic imaging far-focus compound imaging reversal-squart zero-cross factor lag-one coherence-based zero-cross factor

1. Introduction

Ultrasound imaging has been widely used in clinical examination because of portability, safety, and low cost. However, there are still some main challenges of imaging quality that remain in conventional ultrasound systems. Ultrasound compound imaging mode has been widely studied for improving imaging quality. The concept of compound imaging is mainly associated with a superposition of several low-quality image frames in an attempt to cancel out noise, reduce artifacts, and thus improve the contrast and resolution.

In recent years, a variety of compound imaging modes have been proposed and they used different emission schemes. These imaging modes show different performance in terms of imaging quality, frames and complexity. Synthetic aperture imaging (SA) has been extensively investigated. SA achieves a uniform lateral resolution in the region-of-interest (ROI), but suffers from a poor SNR. To overcome the limitations of SA, other SA-based methods have been developed. SA method with bidirectional pixel-based focusing (SA-BiPBF) method uses a subaperture (e.g., 64 channels) for transmitting ultrasound waves in exactly the same manner as in the conventional B-mode imaging [1]. Full aperture received far-focused pixel-based (FrFPB) imaging is an improved version of SA-BiPBF, which uses all elements to receive the echo signals to achieve better image resolution [2].

Aimed at improving image quality of SA-based methods, we hereby propose an improved imaging mode named far-focus compound (FSC) imaging. In transmission, it uses the full aperture to transmit the focused beam to ensure image resolution and emission of sound field energy. In reception, the full aperture is used to receive the reflected beam to ensure the image quality. However, as a result of the nonadaptive delay-and-sum (DAS) beamforming process, its contrast performance is still limited.

Adaptive weighting schemes, such as coherence factor (CF)-based approaches [3, 4, 5, 6], are widely used effective techniques to deal with the weaknesses, resulting in reduced noise and suppressed side lobes. In addition, the zero-cross factor (ZF) for ultrasound is proposed. With the advancement of technology, many ZF-based methods have been developed. Adjustable zero-cross factor (AZF) [2] based on the polarity of echo signal sequence can effectively reduce the noise power. However, AZF cannot scale the noise power precisely, and it cannot used as adaptive weighting factor [2]. More recently, Long et al. [7] proposed a imaging metric, known as the lag-one coherence (LOC), which leverages the spatial coherence between nearest-neighbor array elements to provide a local measure of thermal and acoustic noise. Because spatial coherence is sensitive to all major forms of acoustic clutter as well as random thermal noise, making LOC particularly useful for characterizing and discriminating between backscattered signal and noise [7, 8, 9, 10, 11]. Awaring that FSC still offers limited improvement in SNR. We combine the feature of AZF and LOC to propose a novel method called lag-one coherence-based zero-cross factor (LOCZF) and introduced it into FSC to enhance the image quality. AZF is modified to reversal-squart zero-cross factor (rsZF) at first, and rsZF is suitable for the weighting coefficient. And then LOC that can evaluate the signal coherence accuatly are used to adaptively parameterize the SNR estimation in rsZF. To evaluate the imaging performance, the simulations and experiments were performed and the proposed method was compared with FSC, CF, generalized CF (GCF), rsZF, and LOC.

2. Method

2.1 Proposed far-focus compound (FSC) imaging

FSC imaging is a technique that uses full-aperture transmission with full-aperture reception. The FSC imaging technique uses a full aperture to transmit ultrasound in the same way as conventional focused imaging. As shown in Fig. 1, the full-aperture unit is active at each transmit, the transmitted focused wave propagates in the imaging field, and the full-aperture unit is then used to receive the backscattered echo.

In this way, each transmission can produce a low-resolution image, and finally a high resolution image will be obtained by combining low resolution images from a range of transmissions.

Assuming $N$ is set to the total number of elements and the $m$ th focus is located at ( $x^{f}_{m}$ , $z^{f}_{m}$ ) in $m$ th transmitting event. The time delay $(t_{pt}+t_{pr})$ of echo signal $s_{m,n}(t)$ generated from $m$ th transmit event propagating to the imaging point $p(x_{p},z_{p})$ and back to $n$ th receive element is calculated as:

$\displaystyle t_{pt}={\displaystyle\frac{L_{\textit{MAX}}-\sqrt{(x_{p}-x^{f}_{% m})^{2}+(z_{p}-z^{f}_{m})^{2})}}{c}}$ (1)

where $t_{pt}$ represents the trasmitting time delay and $L_{\textit{MAX}}$ represents the maximum distance between the $m$ th focus and the array element. $c$ is the speed of sound in the medium. $L_{\textit{MAX}}$ is defined as:

$\displaystyle L_{\textit{MAX}}=\max\left(\sqrt{(x_{1}-x^{f}_{m})^{2}+(z_{1}-z^% {f}_{m})^{2}},\sqrt{(x_{N}-x^{f}_{m})^{2}+(z_{N}-z^{f}_{m})^{2}}\right)$ (2)

where ( $x_{1}$ , $z_{1}$ ) and ( $x_{N}$ , $z_{N}$ ) respectively denotes position of the 1th element and the Nth element. Different from SA-BiPBF and FrFPB methods, the emission sound field of FSC method will change with the change of focus. In order to obtain more accurate transmission delay, the Eq. (2) is used to calculate $L_{\textit{MAX}}$ .

$\displaystyle t_{pr}={\displaystyle\frac{\sqrt{(x_{p}-x_{n})^{2}+z^{2}_{p}}}{c}}$ (3)

where $t_{pr}$ represents the receiving time delay and $x_{n}$ denotes the lateral position of the $n$ th element.

In FSC, the number of receiving elements is equal to the number of array elements. The echo signals generated in effective transmit field are used to calculate the imaging value to decrease computational load. The echo signal of imaging point $p$ received by the $n$ th element in the $m$ th effective transmit event can be expressed as $s_{m,n}(p)$ , and it is given by:

$\displaystyle s_{m,n}(p)=\left\{\begin{array}[]{ll}s_{m,n}(t-t_{pr}-t_{pt}),&% \tan(\theta_{m2})\leqslant{\displaystyle\frac{x_{p}-x^{f}_{m}}{|z_{p}-z^{f}_{m% }|}}\leqslant\tan(\theta_{m1})\\ 0,&\text{otherwise}\\ \end{array}\right.$ (4)

where $\theta_{m1}$ and $\theta_{m2}$ are the angle of effective transmit field in the $m$ th transmit event, as shown in Fig. 2. Where $Z_{\max}$ is the maximum imaging depth and $\Delta x$ denotes the pitch of elements. $\theta_{m1}$ and $\theta_{m2}$ are given by:

$\displaystyle\theta_{m1}=\arctan\left({\displaystyle\frac{x_{N}-x^{f}_{m}}{z^{% f}_{m}}}\right)$ (5) $\displaystyle\theta_{m2}=\arctan\left({\displaystyle\frac{x_{1}-x^{f}_{m}}{z^{% f}_{m}}}\right)$ (6)

where $x_{1}$ and $x_{N}$ represent the lateral positions of the 1st and $N$ th element, respectively, and $N$ is set to the total number of elements. According to the Eq. (4), the value of imaging point $p$ in the $m$ th transmit event with a predefined apodization can be given by:

$\displaystyle S_{m}(p)={\displaystyle\frac{1}{N}}\sum_{n=1}^{N}w_{n}\cdot s_{m% ,n}(p)$ (7)

where $w_{n}$ stands for predefined weight and $N$ is the number of receive elements in the $m$ th transmit event. In FSC, $N$ is set to the number of array elements, and it means that all elements are used to receive echo signals at each transmit event.

As the ineffective transmit events will not be used for imaging, using non-zero imaging values of imaging point $p$ to compose a vector $S(p)=[S_{1}(p),S_{2}(p),S_{3}(p)\ldots S_{K}(p)]$ , and $K$ denotes the number of effective transmit events of imaging point $p$ . Then, the output of FSC based on DAS can be expressed as:

$\displaystyle Y_{\textit{FSC}}(p)={\displaystyle\frac{1}{K}}\sum_{k=1}^{K}w_{k% }\cdot S_{k}(p)$ (8)

where $w_{k}$ is the predefined weight, and Hanning window is used in this work.

2.2 AZF and LOC

In ultrasound imaging, the SNR of echo signals varies with the depth of ROI. Zero-crossing point (ZP) has the ability to reflect signal characteristics and variations, and it also can reflect the coherence of the pre-compounded imaging results in ultrasound imaging [5]. Based on this idea, adjustable zeros-cross factor (AZF) has been proposed. According to the definition of ZP and FSC, the value of ZP is obtained as:

$\displaystyle ZP_{k}(p)=\left\{\begin{array}[]{ll}1,&S_{k}(p)\cdot S_{k+1}(p)% \leqslant 0\\ 0,&S_{k}(p)\cdot S_{k+1}(p)>0\\ \end{array}\right.$ (9)

The value of $Z P$ is the summation of $ZP_{k}(p)$ . From Eq. (9), it is easy to know that $Z P$ of noise is seem to be a high value. For $S(p)$ with high SNR, $Z P$ will be close to 0. AZF is defined as:

$\displaystyle\textit{AZF}(p)={\displaystyle\frac{\sum_{k=1}^{K-1}ZP_{k}(p)}{(K% -1)\sigma}}$ (10)

where $\sigma$ is an adjustable coefficient which can directly control the value of $\textit{AZF}(p)$ . $\sigma$ is set from 0 to 1.

In practice, LOC can be calculated by taking the average correlation between pairs of time-delayed channel signals $S_{k}$ and $S_{k+1}$ received at array elements with one-element separation [7]. Therefore, it is given by:

$\displaystyle\textit{LOC}(p)={\displaystyle\frac{1}{M-1}}\sum_{k=1}^{M-1}{% \displaystyle\frac{\sum_{p=p_{1}}^{p_{2}}S_{k}[p]\cdot S_{k+1}[p]}{\sqrt{\sum_% {p=p_{1}}^{p_{2}}S^{2}_{k}[p]\cdot\sum_{p=p_{1}}^{p_{2}}S^{2}_{k+1}[p]}}}$ (11)

where $M$ is the total number of array elements and $p_{1}$ and $p_{2}$ define the bounds of an axial kernel.

2.3 Proposed method

According to the Eq. (10), AZF may not scale the noise power precisely for every imaging point, however LOC leverages the spatial coherence between nearest-neighbor array elements to provide a local measure of thermal and acoustic noise. The former can reduce the noise power very well, but it is not accurately distinguish between noise and incoherent signals, the latter can accurately distinguish between noise and incoherent signals, but the ability to reduce noise is very weak. Based on this idea, lag-one coherence-based zeros-cross factor (LOCZF) is proposed for FSC to improve the image quality. As seen, if $\sigma=$ 1, $\textit{AZF}(p)<$ 1. if $\sigma<$ 1, the $\textit{AZF}(p)$ may be more than 1. For desired signal, $\textit{AZF}(p)$ is a value close to 0, and expecting that the desired signal will not decay. For noise, $\textit{AZF}(p)$ is a value much larger than 1, which is expect to remove the noise. Thus, $\textit{AZF}(p)$ is modified to $\textit{rsZF}(p)$ and $\textit{rsZF}(p)$ is defined as:

$\displaystyle\textit{rsZF}(p)=\left(1-\left({\displaystyle\frac{\sum_{k=1}^{K-% 1}ZP_{k}(p)}{(K-1)\sigma}}\right)^{2}\right)H\left(1-\left({\displaystyle\frac% {\sum_{k=1}^{K-1}ZP_{k}(p)}{(K-1)\sigma}}\right)^{2}\right)$ (12)

where $\sigma$ is an empirical parameter and usually takes a value of 0.6. It does not accurately reflect the characteristics of each point. $H(x)$ is Heaviside function. Therefore, using LOC to adjust the parameter $\sigma$ in real time.

$\displaystyle\sigma=\sqrt{\textit{LOC}(p)}$ (13)

From Eqs (12) and (13), LOCZF can be obtained as shown in Eq. (14):

$\displaystyle\textit{LOCZF}(p)=\left(1-\left({\displaystyle\frac{\sum_{k=1}^{K% -1}ZP_{k}(p)}{(K-1)\sqrt{\textit{LOC}(p)}}}\right)^{2}\right)H\left(1-\left({% \displaystyle\frac{\sum_{k=1}^{K-1}ZP_{k}(p)}{(K-1)\sqrt{\textit{LOC}(p)}}}% \right)^{2}\right)$ (14)

For LOCZF methods, the weighted outputs can be expressed as follows:

$\displaystyle Y_{\textit{LOCZF}}(p)=\textit{LOCZF}(p)\cdot Y_{\textit{FSC}}(p)$ (15)

3. Simulations and experimental setup

3.1 Simulated dataset

A point and cyst mixed phantom were designed in Field II [12, 13] to study performance of the proposed method. For the point target phantom, there are ten points at different depths (range: 15–30 mm). For the cyst target phantom, there are two cysts with different radius. One cyst radius is 2 mm and another cyst radius is 1 mm. In the simulation, the transducer was a linear array, the center frequency was 5 MHz, which had 128 elements and 0.3 mm pitch. 40 MHz sampling frequency was adopted. The sound velocity was 1540 m/s. The focal depth was 50 mm. The parameters used in the simulation are presented in Table 1.

Prior to imaging, a Gaussian-distributed white noise with an SNR of 10 dB was fed into the channel RF data. Figure 4 shows the original echo signal and the signal with noise added, received by the 64th array element during the 64th transmission. It was chosen to 2 for the cutoff frequency $M_{0}$ in GCF. For LOCZF, $C$ in Eq. (13) was empirically set to 0.8.

Table 1
Parameters used in simulations and experiments

Parameter	Value
Number of elements	128
Number of transmit elements	128
Number of receive elements	128
Element height	5 mm
Element width	0.25 mm
Pitch	0.3 mm
Kerf	0.05 mm
Focal depth	50 mm
Center frequency	5 MHz
Sampling frequency	40 MHz
Speed of sound	1540 m/s
Pulse excitation cycle	2

3.2 Experimental dataset

To evaluate the imaging performance of the proposed method, two experimental phantom datasets and one carotid artery dataset were utilized. The phantom data was gathered using a Sonix-Touch data acquisition system from a linear array transducer (L14-5/38) connected to a KS107BD phantom (Chinese Academy of Sciences, China). One dataset was used for point target imaging, while the other was utilized for anechoic cyst imaging. The carotid artery dataset was acquired from a male volunteer using the same transducer and acquisition system. The system employed is an open platform, allowing manual adjustment of parameters such as the number of transmitting and receiving elements, pulse excitation cycle, center frequency, and sampling frequency. Specifically, a 128-element linear array transducer was employed, with all elements active during each transmission. After configuring the parameters, scanning was performed on the region of interest, and the data were collected using a data acquisition (DAQ) device connected to the Sonix-Touch system. The specific transducer parameters and experimental setup are outlined in Table 1. Similarly, the parameter options and usage for different methods were the same as those used in the simulations. Each image was displayed at a 60-dB dynamic range.

3.3 Image quality metrics

Image resolution, contrast ratio (CR), contrast-to-noise ratio (CNR), generalized contrast-to-noise ratio (gCNR) and speckle signal-to-noise ratio (sSNR) used as performance evaluation metrics. Resolutions are gauged by evaluating the full width at half maximum (FWHM, $-$ 6 dB beam width) of the main lobe width for point targets [14]. CR, CNR and sSNR will be made to assess the performance of different methods in logarithmic images for cyst images, which are in definition as [15, 16, 17, 18]

$\displaystyle CR=|\mu_{b}-\mu_{i}|$ (16) $\displaystyle\textit{CNR}={\displaystyle\frac{|\mu_{i}-\mu_{b}|}{\sigma_{b}}}$ (17) $\displaystyle\textit{sSNR}={\displaystyle\frac{\mu_{b}}{\sigma_{b}}}$ (18)

where $\mu_{i}$ and $\mu_{b}$ refer to the mean values within the cyst target and the speckle background, respectively, while $\sigma_{i}$ and $\sigma_{b}$ are the corresponding standard deviations.

The gCNR can assess contrast enhancement effects independent from the dynamic range alternation [19]. And gCNR based on the overlap area of the probability density function inside and outside the target area is defined as

$\displaystyle\textit{gCNR}=1-\int\min\{p_{c}(x),p_{b}(x)\}dx$ (19)

where $x$ is the pixel intensity, the $p_{c}(x)$ and $p_{b}(x)$ are the probability distribution of the cyst target and speckle background.

4. Results

4.1 Simulated point and cyst

Simulated point and cyst images formed using different imaging methods are displayed in Fig. 5 over a 60 dB dynamic range. Lateral variations of the points at the depth of 19 mm are shown in Fig. 6. Figure 6 indicates that CF offers the narrowest main lobe width. Furthermore, FSC, rsZF, LOC, and LOCZF offers the same main lobe width. Table 2 gives the corresponding statistical results of lateral FWHM. CF obtains the lowest FWHM value among all methods. FSC, rsZF, LOC, and LOCZF obtain the same FWHM value.

Figure 5a shows that the internal noise of the cyst target in the FSC image is larger than in other imaging methods. Observing from Fig. 5b and c that CF and GCF images show some dark area artifacts, and the image background quality is poor. Compared with CF and GCF, the background of LOC, rsZF and LOCZF images in Fig. 5d–f is more uniform, while the image of LOCZF has the best visual effect.

Table 2

Lateral FWHM at 19 mm depth, CR, CNR, gCNR and sSNR values of different methods in simulation

Method	FWHM	CR (dB)	CNR	gCNR	sSNR
FSC	0.36 mm	23.75/23.62	4.23/4.08	0.9413	5.38/5.24
CF	0.28 mm	49.85/48.85	4.23/4.03	0.8672	1.88/1.79
GCF	0.39 mm	39.32/38.74	5.04/4.88	0.9448	3.01/2.93
LOC	0.36 mm	55.59/56.44	8.45/8.46	0.9850	4.21/4.14
rsZF	0.36 mm	33.11/32.73	5.12/4.89	0.9867	4.51/4.36
LOCZF	0.36 mm	69.60/69.70	11.34/11.04	0.9906	4.83/4.71

CR, CNR, gCNR and sSNR values of all images are calculated. The cyst and background selected to calculate the metrics are illustrated in Fig. 5a. The values are given in Table 2. The CR of FSC is the lowest, but its sSNR are the highest, which means that FSC obtained the best speckle quality. Compared with CF, LOCZF obtains improvements of 41.1% in CR, 170.9% in CNR, 159.9% in sSNR, and its sSNR are only slightly lower than FSC. For rsZF, CR is reduced by 33.3%, CNR is increased by 21.1%, and sSNR is increased by 141.4%. The CR of LOC is improved slightly, and its CNR and sSNR are lower than LOCZF. This indicates that LOCZF not only improves image contrast but also preserves speckle. Furthermore, LOCZF obtains a good gCNR, which is higher than other methods.

4.2 Experimental point

The experimental images of point targets obtained by different methods are shown in Fig. 7. The CF and GCF images in Fig. 7b and c reveal that they make the speckle darker and inject black-spot artifacts in the speckle. Figure 7d and f present that the LOC-based, rsZF-based and LOCZF-based methods better retain the speckle pattern than CF and GCF.

Figure 8 displays the experimentally obtained lateral variations of the two point targets located at ( $Z=$ 18.5 mm) and ( $Z=$ 28.5 mm). As shown in Fig. 8, the main lobe width of CF is slightly lower than that of other methods. The GCF-based, LOC-based, rsZF-based and LOCZF-based methods provide similar main lobe widths. The side lobes of CF and GCF are lower than that of other methods, that is, the side lobes of CF and GCF are suppressed. Table 3 gives the results of lateral FWHM values. CF has the smallest FWHM value among all methods. The methods of FSC, GCF, LOC, rsZF and LOCZF obtain the same FWHM values, which means that the resolution performances of FSC, GCF, LOC, rsZF, and LOCZF are almost the same.

Table 3

Lateral FWHM of experimental point images formed using different methods

Method	18.5 mm depth	28.5 mm depth
FSC	0.38 mm	0.42 mm
CF	0.36 mm	0.41 mm
GCF	0.38 mm	0.42 mm
LOC	0.38 mm	0.42 mm
rsZF	0.38 mm	0.42 mm
LOCZF	0.38 mm	0.42 mm

4.3 Experimental cyst

The experimental cyst images formed with different methods are shown in Fig. 9. Compared with FSC, all methods except rsZF obtain better contrast and good noise suppression effect in cysts. CF and GCF seem to have a high contrast, but the image quality of the background region is declined due to damaged speckle pattern. LOC and LOCZF provide good comprehensive imaging performance in terms of background areas and cysts.

The CR, CNR, gCNR and sSNR values of experimental images are listed in Table 4. The selected cysts and background areas that are used to calculate are indicated in Fig. 9a. It can be seen that although FSC has the lowest CR, its sSNR are the highest. Compared with CF, LOCZF obtains an improvement of 44.3% in CR, 171.8% in CNR, 135.1% in sSNR, and its sSNR are only slightly lower than FSC. For rsZF, CR is reduced by 38.9%, CNR is increased by 8.5%, and sSNR is increased by 116.8%. The CR of LOC is reduced by 16.8%, and its CNR and sSNR are lower than LOCZF. This indicates that LOCZF not only improves image contrast but also preserves speckle. And LOCZF obtains the highest gCNR value than other methods in the experiment.

Table 4
CR, CNR, gCNR and sSNR values of different methods in experiment

Method	CR (dB)	CNR	gCNR	sSNR
FSC	16.11	2.83	0.7900	6.21
CF	35.74	2.94	0.7777	2.25
GCF	32.08	3.29	0.8051	2.98
LOC	29.75	4.60	0.8444	4.87
rsZF	21.82	3.19	0.8076	4.88
LOCZF	51.56	7.99	0.8462	5.29

Table 5

CR, CNR, gCNR and sSNR values of different methods in carotid artery

Method	CR (dB)	CNR	gCNR	sSNR
FSC	11.58	1.79	0.6420	3.62
CF	23.83	1.59	0.5838	0.65
GCF	24.56	2.20	0.7046	1.05
LOC	19.32	2.79	0.7555	2.99
rsZF	15.64	2.23	0.7132	3.15
LOCZF	24.63	3.63	0.7583	3.32

4.4 In-vivo experiment

To further evaluate the imaging performance of different weighting methods, the in-vivo experiment was also conducted. We chose the carotid artery as the imaging object. Compared to the results of the simulated and experimental phantom studies, the imaging results of the carotid artery may be more affected by phase aberrations because of the surrounding complex tissue. The images of the carotid horizontal section obtained by different methods are shown in Fig. 10. It can be seen that the noises inside the artery in CF, GCF, LOC and LOCZF images are suppressed effectively, and the background tissue in CF and GCF image is grainier compared to LOCZF image. The noise inside the artery in rsZF image is large. The background tissue of the LOCZF image is clearly visible and the arterial wall can be easily distinguished.

Table 5 lists CR, CNR, gCNR and sSNR values of in-vivo carotid artery images. Compared with FSC, CR of CF and GCF is significantly improved, however their CNR and sSNR are significantly decreased. Compared with CF and GCF, the CR of LOCZF is slightly higher, and CNR and sSNR of LOCZF are also higher. Compared with rsZF, LOCZF obtains an improvement of 57.5% in CR. CR, CNR, and sSNR of LOCZF are higher to LOC. The gCNR values of LOCZF is higher than other methods.

5. Discussion

In this paper, a new ultrasonic imaging mode, FSC, is proposed for the first time. In order to better reflect the image performance of FSC, we compare the imaging mode of FSC with the imaging mode of FrFPB, SA-BiPBF and line scanning. Figure 11 shows the simulated point images obtained by different imaging methods. It can be seen in Fig. 11d that the width of the main lobe obtained by FSC is the narrowest. Figure 12 presents the horizontal FWHM values of the point target at different depths quantitatively, showing the performance of different methods more intuitively, in which FSC obtains the smallest FWHM value among all methods. This shows that FSC has the best resolution. This superiority of FSC is due to the utilize of full-aperture transmission and full-aperture reception.

Imaging results show that CNR, sSNR, and CR of LOCZF is superior to other weighting coefficients except unweighted FSC. Although traditional CF-based beamformer can improve the image contrast, the beamformer based on coherence measurement will lead to negative problems such as dark-region artifacts and speckle variance increases [20]. CR and CNR of LOCZF are better than FSC, but SSNR is slightly worse than unweighted FSC. This is because the background standard deviation of LOCZF increases quite a bit and the background strength decreases a bit. However, the CR of LOCZF is increased by a lot. LOCZF outperforms the other weighting factors in CNR because it gets a higher CR, and CNR is obtained by dividing CR by the variance of the background tissue.

For the adaptive weighting method, we expect that the weighting coefficients for both background tissue and strong echo targets are 1, which means that the intensity of the imaging point is not attenuated, and the background speckle characteristics are perfectly preserved. For noise, the weighting coefficient is 0, which can completely suppress noise. For the simulation target in this paper, the ideal weighting coefficient is shown in Fig. 13a. Figure 13d–f are direct output images of LOC, rsZF, and LOCZF, respectively. The differences between each method and the expected weighting coefficients can be clearly seen in this figure, with LOCZF being the closest to the expected weighting coefficients.

Figure 14d–f show the difference between the desired weighting coefficient and other weighting coefficients, which reflects the imaging deviation. It can be clearly seen that the deviation of LOCZF is also the smallest throughout the imaging area. Figures 13 and 14 clearly illustrate the performance differences between these methods.

In order to improve the image quality of FSC, LOCZF is proposed as an adaptive weighting factor. Simulation and experimental results show that compared with FSC beamformers, the proposed adaptive weighting factor can not improve image resolution, but it can improve image contrast. This is because that the features of LOC and rsZF do not affect image resolution. The LOC value of the scattering target with high coherence is close to 1, which will not affect the imaging width of scattering points [21]. Therefore, LOC has no effect on the image resolution. When using LOC to adjust rsZF, the image resolution will not be affected.

As shown in Figs 5 and 9, LOCZF can reduce noises in cyst targets and maintain the background brightness. Compared with FSC, CR value can be significantly improved. For experimental cysts, CR improvement is 44.9%. From the in-vivo result, CR improvement is 34.9%. This is because that LOC is sensitive to the intrinsic properties of target and background regions, so LOC can maintain the background brightness [22]. Although rsZF is also sensitive to the intrinsic properties of target and background regions, noise suppression of rsZF is insufficient. Because LOC is sensitive to all major forms of ultrasonic clutter and noise originated from phase aberration, reverberation clutter, off-axis scattering, and thermal noise [7], so noise suppression was enhanced by adjusting rsZF with LOC.

The proposed adaptive weighting approach can improve image quality, but the computational cost is quite high. Given a linear transducer array with $N(n<N)$ array elements, with a pixel $p$ imaged. The computational complexity of CF is $O(N)$ , the computational complexity of GCF is $O(N\log_{2}N)$ , the computational complexity of rsZF is $O(n)$ , the computational complexity of LOC is $O(n\times(2L+1)^{2})$ . However, the computational complexity of LOCZF is $O(n\times(2L+1)^{2})$ , where $L$ is an empirical constant. Generally speaking, compared with the improvement of image quality, the increase of computational complexity is acceptable.

6. Conclusion

In this paper, we first propose a new ultrasound imaging mode, FSC, and then propose LOCZF as an adaptive weighting factor to further improve the image quality. The proposed method has been evaluated through simulated and experimental datasets and was compared with CF, GCF, LOC, and rsZF. Simulation and experimental results show that the proposed LOCZF not only improves CR greatly, but also retains the speckle pattern. LOCZF shows improved gCNR performance. In addition, the LOCZF method shows good performance in experiments. The proposed method can be used as an effective weighting technique for improvement of image quality in ultrasound imaging.

Footnotes

Acknowledgments

This work was supported in part by National Natural Science Foundation of China (62101173, 62071165), in part by Fundamental Research Funds for the Central Universities (JZ2021HGTB0074, JZ2023HGQA0079).

Conflict of interest

None to report.

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Far-focus compound ultrasound imaging with lag-one coherence-based zero-cross factor

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSION:

Keywords

1. Introduction

2.1 Proposed far-focus compound (FSC) imaging

3.1 Simulated dataset

Table 1 Parameters used in simulations and experiments

3.3 Image quality metrics

4.1 Simulated point and cyst

Table 4 CR, CNR, gCNR and sSNR values of different methods in experiment

6. Conclusion

Footnotes

Acknowledgments

Conflict of interest

References

Table 1
Parameters used in simulations and experiments

Table 4
CR, CNR, gCNR and sSNR values of different methods in experiment