The goal of beamforming is to focus ultrasound energy to one location only, but this is not truly achievable with standard delay and sum beamforming. This gives rise to off-axis sidelobes and clutter. These sidelobes or clutter inherent in ultrasound imaging are undesirable side effects because they degrade image quality by lowering CNR and the detectability of small targets. Improving the contrast of ultrasound has many clinically significant applications. In breast ultrasound, the main purpose is to differentiate solid and cystic masses [1]. Simple anechoic cysts with fill-in caused by multiple scattering, reverberations, and clutter can be misclassified as malignant lesions. Levels of fill-in are increased in the presence of aberrations caused by intermittent layers of fat and tissue. Delineation of carcinoma may also be improved with better signal processing methods that improve contrast. Similar problems arise when imaging other soft tissue. For hepatic imaging, visualization of cystic liver lesions and dilated bile ducts can be improved [2]. The visualization of prostate cancer may be improved because prostate cancer is usually hypoechoic [3].
波束成形的目标是将超声能量聚焦于一个位置，但使用标准的延迟和求和波束成形无法真正实现这一点。这会导致轴外旁瓣和杂波的产生。超声成像中固有的这些旁瓣或杂波是不希望出现的副作用，因为它们通过降低对比度噪声比和小目标的可检测性来降低图像质量。提高超声的对比度有许多临床上重要的应用。在乳腺超声中，主要目的是区分实性和囊性肿块。由于多次散射、回声和杂波引起的填充效应，简单的无回声囊肿可能被误分类为恶性病变。在由间歇性脂肪和组织层引起的像差存在时，填充效应的水平会增加。通过改善提高对比度的信号处理方法，也可能改善癌症的界定。成像其他软组织时也会出现类似问题。对于肝脏成像，可以改善囊性肝病变和扩张的胆管的可视化。因为前列腺癌通常是低回声的，所以前列腺癌的可视化可能会得到改善。

One way to improve CNR is to reduce sidelobe and clutter levels by applying a weighting or shaping function such as a Hanning or Hamming apodization across the transmit-and-receive apertures. These types of weighting functions are called linear apodization functions because the same weighting is applied to the aperture independent of depth or of imaging line. As a trade-off, they lower the sidelobes at the expense of worse mainlobe lateral resolution. To avoid making this trade-off, there have been several publications in nonlinear sidelobe suppression methods that aim for little or no loss in mainlobe resolution while achieving low clutter levels commonly associated with apodization [4]–​[7].
提高CNR的一种方法是通过在发射和接收孔径上应用加权或成形函数，如汉宁或哈明消光函数，来降低旁瓣和杂波水平。这些类型的加权函数被称为线性消光函数，因为相同的加权被应用于孔径，而不考虑深度或成像线。作为一种权衡，它们通过牺牲主瓣横向分辨率来降低旁瓣。为了避免做出这种权衡，已经有几篇关于非线性旁瓣抑制方法的出版物，这些方法旨在在实现低杂波水平的同时，几乎不损失主瓣分辨率，这通常与消光相关。

In recent work, Guenther and Walker developed optimal apodization functions using constrained least squares theory [4], [5]. This method creates apodization functions with the goal of limiting the energy of the point spread function (PSF) outside a certain area and maintaining a peak at the focus. A point target simulation was performed using a linear array with 192 elements with 200 μm element pitch and a transmit frequency of 6.5 MHz. Using this method, a 5 to 10 dB reduction in sidelobe levels compared with a Hamming apodization was achieved. Wang used a comparator to select the minimum magnitude from 2 or more sets of data using various apodization methods, such as uniform, Hanning, or Hamming [6]. By taking the minimum magnitude on a pixel-by-pixel basis, this method preserves the mainlobe resolution of the uniformly apodized data and lowers sidelobes similar to a Hanning or Hamming apodized data. Stankwitz developed a spatially variant nonlinear apodization (SVA) technique, which uses the lateral phase differences between Hanning and uniformly apodized data to distinguish between mainlobe and clutter signals. This is accomplished by taking advantage of the properties of raised-cosine weighting functions and finding the optimal apodization function on a pixel-by-pixel basis [7].
在最近的工作中，Guenther和Walker使用受限最小二乘理论开发了最优化的消光函数。这种方法创建了消光函数，目的是限制点扩散函数（PSF）在某一特定区域外的能量，并在焦点处保持一个峰值。使用具有192个元素的线性阵列进行了点目标模拟，元素间距和传输频率分别为6.5 MHz。使用这种方法，与汉明消光相比，旁瓣电平实现了5到10 dB的降低。Wang使用比较器从两个或更多组数据中选择最小幅度，使用了各种消光方法，如均匀、汉宁或汉明。通过逐像素取最小幅度，这种方法保留了均匀消光数据的主瓣分辨率，并降低了旁瓣，类似于汉宁或汉明消光数据。Stankwitz开发了一种空间变化的非线性消光（SVA）技术，该技术使用汉宁和均匀消光数据之间的横向相位差异来区分主瓣和杂波信号。 这是通过利用升余弦加权函数的特性，并在像素级别上找到最佳的消光函数来实现的。

An ideal contrast improvement method would greatly improve contrast such that lesions are easily visualized without significantly increasing computational complexity or worsening lateral and/or temporal resolution. In this paper, we present a target-dependent clutter suppression method using pairs of apodization functions. By using certain pairs of apodization functions, we can pass mainlobe signals and attenuate clutter signals using normalized cross-correlation coefficients of RF signals in the axial direction. The amount of attenuation is proportional to the amount of clutter in the signal. A target-dependent weighting matrix is created that will be multiplied to the standard beamformed image. In a point target simulation, using a linear array with 128 elements with element pitch of 308 μm and a transmit frequency of 5 MHz, this technique lowers clutter levels by more than 40 dB compared with standard beamformed data with a uniform apodization while keeping the same mainlobe resolution with a minimal computation load.
理想的对比度改善方法将大幅提高对比度，使得病变容易被观察到，同时不会显著增加计算复杂性或恶化横向和/或时间分辨率。在本文中，我们提出了一种使用一对透镜函数对的目标依赖型杂波抑制方法。通过使用特定的透镜函数对，我们可以通过轴向方向的射频信号的归一化互相关系数，传递主瓣信号并衰减杂波信号。衰减的量与信号中的杂波量成正比。创建了一个目标依赖的加权矩阵，将乘以标准波束形成图像。在一个点目标模拟中，使用具有128个元素的线性阵列，元素间距为308μm，发射频率为5 MHz，与使用均匀透镜的标准波束形成数据相比，这种技术将杂波水平降低了40 dB以上，同时保持了相同的主瓣分辨率，并且计算负担最小。

Assuming linearity, any ultrasound echo signal can be thought of as the sum of 2 signals: one signal is the mainlobe contribution that is desired and one signal from the sidelobes, grating lobes, and other forms of clutter that reduce image contrast. The amount of mainlobe contribution and sidelobe contribution depends on 2 factors: 1) the ratio of the mainlobe amplitude to the sidelobe amplitude and 2) the strength of the scatterers within the mainlobe versus the strength of the scatterers in the clutter region. To improve contrast, one would like to remove or at least minimize contributions from clutter. Our approach to removing clutter is to distinguish the mainlobe dominated signals from clutter signals by developing 2 point spread functions using 2 different apodization functions. These 2 apodization functions give similar mainlobe signals and very different clutter patterns. Therefore, echoes from a target such as speckle or a point target that are comprised primarily of mainlobe components will look similar to each other, but echoes from a target such as a cyst that are mainly clutter will appear different from each other. Signals from a target that consists of a comparable contribution from both mainlobe and clutter will be partially similar.
假设线性，任何超声回波信号都可以被认为是2个信号的总和：一个是期望的主瓣贡献信号，另一个来自副瓣、栅瓣以及其他形式的杂波，这些都会降低图像对比度。主瓣贡献和副瓣贡献的量取决于两个因素：1）主瓣振幅与副瓣振幅的比例；2）主瓣内散射体的强度与杂波区域内散射体的强度。为了提高对比度，人们希望去除或至少最小化来自杂波的贡献。我们去除杂波的方法是通过开发两个不同的权函数来使用两个点扩散函数区分主瓣主导信号和杂波信号。这两个权函数产生相似的主瓣信号和非常不同的杂波模式。因此，主要由主瓣组成的目标（如散斑或点目标）的回声看起来彼此相似，但主要是杂波的目标（如囊肿）的回声看起来彼此不同。 来自一个目标的信号，由主瓣和杂波的相当贡献组成，将部分相似。

The degree of similarity can be quantified using normalized cross-correlation between the 2 signals RX1 and RX2 from 2 PSFs. Normalized cross-correlation (NCC) is performed using segments of RF data along the axial direction at zero lag. The normalized cross-correlation coefficient ρ at zero lag is calculated for every sample and used as a target-dependent pixel-by-pixel weighting matrix, which passes mainlobe dominated signals and attenuates clutter dominated signals:

View Source\rho(i, j)= {\sum\limits^{i+A}_{k=i-A}RX1(k, j)RX2(k,j) \over \sqrt{\sum\limits_{k=i-A}^{i+A}RX1(k,j)^{2}}\sqrt{\sum\limits_{k=i-A}^{i+A}RX2(k,j)^{2}}}. \eqno{\hbox{(1)}}

相似度可以通过两个点扩散函数（PSFs）中的两个信号RX1和RX2之间的归一化互相关来量化。归一化互相关（NCC）是使用沿轴向方向的射频数据段在零延迟下进行的。零延迟处的归一化互相关系数 ρ 对每个样本进行计算，并用作目标依赖的逐像素加权矩阵，该矩阵通过主瓣主导的信号并衰减杂波主导的信号：

ρ(i,j)=∑k=i−Ai+ARX1(k,j)RX2(k,j)∑k=i−Ai+ARX1(k,j)2−−−−−−−−−−−−−√∑k=i−Ai+ARX2(k,j)2−−−−−−−−−−−−−√.(1)

View Source\rho(i, j)= {\sum\limits^{i+A}_{k=i-A}RX1(k, j)RX2(k,j) \over \sqrt{\sum\limits_{k=i-A}^{i+A}RX1(k,j)^{2}}\sqrt{\sum\limits_{k=i-A}^{i+A}RX2(k,j)^{2}}}. \eqno{\hbox{(1)}} 然后，后波束形成的射频数据乘以这个加权矩阵。

In (1), index i indicates the ith sample in image line j. The total cross-correlation segment length is 2A+1 samples. Normalized cross-correlation coefficients range from −1 to 1. Two signals are identical if the cross-correlation coefficient is 1, and they are considered uncorrelated if the coefficient is near or below zero. Signals would be somewhat correlated if ρ is in between 0 and 1. In the proposed method, if the coefficient is greater than or equal to a set threshold value ε>0, then the sample value will be multiplied by the cross-correlation coefficient. If the coefficient is less than the threshold value ε, the sample value is multiplied by the threshold value ε. This algorithm is called dual apodization with cross-correlation or DAX. A general system block diagram is shown in Fig. 1.
在 (1) 中，索引 i 表示图像行 j 中的第 i 个样本。总的互相关段长度是 2A+1 个样本。归一化互相关系数的范围从-1到1。如果互相关系数为1，则两个信号是相同的；如果系数接近或低于零，则认为它们是不相关的。如果 ρ 在0和1之间，则信号会有些相关。在提出的方法中，如果系数大于或等于设定的阈值 ε>0 ，则样本值将乘以互相关系数。如果系数小于阈值 ε ，样本值将乘以阈值 ε 。这个算法被称为双重软化与互相关，或DAX。一个通用的系统块图显示在 Fig. 1 中。

Fig. 1.  图 1.

General system block diagram for dual apodization with cross-correlation (DAX). Numbers indicate steps described in the text. RX1 and RX2 are 2 data sets created with 2 apodization functions. *The combined RF data can be obtained by taking the minimum magnitude of RX1 and RX2 or the sum of RX1 and RX2.
双重消光与互相关（DAX）的通用系统框图。数字表示文本中描述的步骤。RX1和RX2是使用2个消光函数创建的2个数据集。*通过取RX1和RX2的最小幅度或RX1和RX2的和，可以获得组合的射频数据。

Show All 显示全部

In Fig. 1, the delayed data are processed with 2 receive apodization functions to create beamformed RF data sets RX1 and RX2. RX1 and RX2 can be combined in different ways. One way to combine them is through a minimum function as done in dual apodization described by Wang and Fienup [6], [7]. This min function is used to select the minimum magnitude at each sample between the 2 data sets. Another way to combine them is to add them. This is the case when the 2 apodization functions are complementary, a scenario shown later in this section. Simply adding the 2 data sets from the complementary apodization functions would give us the same data from a standard receive aperture. If the cross-correlation value is less than a threshold value ε, the value will be replaced with the set threshold value

View Source{\rm DAX}\ {\rm CC} =\cases{ \rho,&$\rho \geq \varepsilon $\cr \varepsilon, &$\rho < \varepsilon $}, \eqno{\hbox{(2)}}

在 Fig. 1 中，延迟数据通过2个接收孔径加权函数处理，以创建形成波束的射频数据集RX1和RX2。RX1和RX2可以通过不同的方式组合。一种组合方式是通过最小函数，如王和Fienup在 [6] ， [7] 中描述的双重孔径加权所做的那样。这个最小函数用于在两个数据集之间的每个样本中选择最小幅度。另一种组合方式是将它们相加。当2个孔径加权函数互补时，就是这种情况，这一场景将在本节后面展示。简单地将来自互补孔径加权函数的2个数据集相加，将给我们与标准接收孔径相同的数据。如果交叉相关值小于阈值 ε ，该值将被替换为设定的阈值

DAX CC={ρ,ε,ρ≥ερ<ε,(2)

View Source{\rm DAX}\ {\rm CC} =\cases{ \rho,&$\rho \geq \varepsilon $\cr \varepsilon, &$\rho < \varepsilon $}, \eqno{\hbox{(2)}} ，其中 ρ 使用 (1) 计算。这个信号被认为主要是杂波，需要被抑制。具有主瓣和杂波相当混合的信号将在 ε 和1之间接收幅度减小。交叉相关矩阵乘以组合的射频数据（*在 Fig. 1 中）。

The detailed steps to acquire a DAX processed image are as follows:
获取DAX处理图像的详细步骤如下：

1. A subaperture (in this paper, 64 elements) transmits a focused beam into the target. Echoes are collected from the same 64 elements.
   本文中的一个子孔径（64个元素）向目标发射一个聚焦的光束。回声由相同的64个元素收集。

2. In receive, we beamform using our first apodization function to create data set RX1.
   在接收时，我们使用我们的第一个声阻抗函数进行波束成形，以创建数据集RX1。

3. Likewise, a second apodization function is used to create data set RX2.
   同样，第二个调制函数被用来创建数据集RX2。

4. These 2 data sets are used to create the combined RF data (* in Fig. 1). The combined RF data can be obtained by taking the minimum magnitude of RX1 and RX2 or the sum of RX1 and RX2.
   这两个数据集被用来创建组合的RF数据（*在 Fig. 1 中）。组合RF数据可以通过取RX1和RX2的最小幅度或RX1和RX2的和来获得。

5. A cross-correlator calculates a normalized cross-correlation value for each pixel. Typically 2 to 3 wavelengths are used as a segment size for cross-correlation.
   交叉相关器为每个像素计算一个归一化的交叉相关值。通常使用2到3个波长作为交叉相关的段大小。

6. The value is sent to a thresholding operator. If the value is less than or equal to ε, then replace it with ε. If it is greater than ε, then leave it unchanged.
   该值被发送到一个阈值操作符。如果该值小于或等于 ε ，则将其替换为 ε 。如果它大于 ε ，则保持不变。

7. The resulting cross-correlation matrix is multiplied by the combined RF data from step 4.
   得到的互相关矩阵与第4步中合并的RF数据相乘。

8. The DAX RF data can undergo further signal processing such as bandpass filtering, envelope detection, log-compression, and scan conversion.
   DAX RF数据可以经过进一步的信号处理，如带通滤波、包络检测、对数压缩和扫描转换。

We investigated the performance of 4 pairs of apodization functions, where each pair has a well-correlated mainlobe response and a different or uncorrelated sidelobe response. All methods use echo data sets formed from each apodization and calculate a weighting matrix by cross-correlating image pairs. All apodization pairs have the same goal of suppressing clutter levels, thus increasing CNR, while maintaining mainlobe resolution.
我们研究了4对消光函数的性能，每对都具有高度相关的主瓣响应和不同或不相关的旁瓣响应。所有方法使用由每个消光形成的回声数据集，并通过交叉相关图像对来计算加权矩阵。所有消光对都有相同的目标，即抑制杂波水平，从而提高对比噪声比，同时保持主瓣分辨率。

A. Apodization Scheme 1: Uniform and Hanning
A. 调制方案1：均匀和汉宁

Motivated by Stankwitz [7], our first choice is using a pair of apodization functions that are common in ultrasound imaging practice. An aperture with a uniform amplitude weighting or a rect apodization function gives a sinc function-shaped beam. This will lead to sidelobes at −26 dB. With an apodization function smoother than uniform apodization such as Hanning apodization, the sidelobe level is lowered from −26 dB to −57 dB but has a larger −6 dB beamwidth compared with uniform weighting (Fig. 2).
受Stankwitz启发，我们的首选是使用一对在超声成像实践中常见的消光函数。具有均匀幅度加权或矩形消光函数的孔径会产生一个sinc函数形状的波束。这将导致侧瓣在-26 dB。使用比均匀消光更平滑的消光函数，如汉宁消光，侧瓣级别从-26 dB降低到-57 dB，但与均匀加权相比，-6 dB波束宽度更大。

Fig. 2.  图 2.

Uniform and Hanning weighted apertures in continuous wave (CW) mode.
连续波（CW）模式下的均匀和汉宁加权孔径。

Show All 显示全部

We can circumvent this trade-off between mainlobe width and sidelobe level, by axially cross-correlating segments of RF data from the 2 data sets obtained using these 2 apodization methods. The RF signals in the sidelobes of the beamformed point target image of these 2 data sets are quite different, giving near zero or negative cross-correlation values. The cross-correlation coefficient at each image sample is calculated. After thresholding, this matrix becomes the weighting matrix, which can be multiplied to the combined RF data at each sample. Fig. 3(a) shows 2 apertures where the first receive aperture has a uniform weighting, and where the second receive aperture has a Hanning apodization.
我们可以通过轴向交叉相关这两种消光方法得到的2个数据集中的射频数据段来规遍这种主瓣宽度和旁瓣电平之间的权衡。这两个数据集中波束形成的点目标图像的旁瓣中的射频信号相当不同，产生接近零或负的交叉相关值。计算每个图像样本处的交叉相关系数。经过阈值处理后，这个矩阵成为加权矩阵，可以乘以每个样本处的组合射频数据。展示了两个孔径，其中第一个接收孔径具有均匀加权，而第二个接收孔径具有汉宁消光。

Fig. 3.  图 3.

All algorithms use a common uniform transmit aperture. The lateral location of the focus is marked with the arrow. The interelement distance, or pitch, is one wavelength. Four pairs of receive apertures used with DAX: (a) uniform and Hanning, (b) common midpoint, (c) random, and (d) alternating pattern.
所有算法使用一个通用的均匀发射孔径。焦点的侧向位置用箭头标记。元素间距离，或称为间距，是一个波长。与DAX一起使用的四对接收孔径：(a) 均匀和汉宁，(b) 公共中点，(c) 随机，以及 (d) 交替模式。

Show All 显示全部

D. Apodization Scheme 4: Alternating
D. 调制方案4：交替

In this scheme, the first receive aperture has alternating elements enabled. The second receive aperture will use the alternating elements that are not used in the first receive aperture. With these 2 apodizations, we purposely create grating lobes that are 180 degrees out of phase with each other. Then, by using cross-correlation, we can distinguish between signals coming from a mainlobe and clutter signals. In our current scheme, signals with cross-correlation coefficients less than 0.001 are multiplied by 0.001 or reduced by 60 dB. Echoes with higher cross-correlation coefficients have more mainlobe signal and are multiplied by the cross-correlation coefficient.
在这个方案中，第一个接收孔径启用了交替的元素。第二个接收孔径将使用第一个接收孔径未使用的交替元素。通过这两种透镜调制，我们故意创建了互相相位相差180度的光栅瓣。然后，通过使用互相关，我们可以区分来自主瓣的信号和杂散信号。在我们当前的方案中，互相关系数小于0.001的信号被乘以0.001或减少60 dB。具有更高互相关系数的回声含有更多主瓣信号，并且被乘以互相关系数。

Fig. 3(d) is an illustration of a pair of receive apertures with a pitch of one wavelength λ. RX1 uses an alternating pattern of 2 elements on, 2 elements off. RX2 uses the opposite alternating pattern of 2 elements off, 2 elements on. These receive apertures are essentially sparse arrays with a 4 wavelength pitch. Thus, grating lobes are expected to be present in the PSF. The location of the nth grating lobe is given by

θn=sin−1(nλd),(3)

View Source\theta_{n}={\hbox{sin}}^{-1}\left({n\lambda\over d}\right),\eqno{\hbox{(3)}}where n is the nth grating lobe, λ is the ultrasound wavelength, and d is the interelement distance or pitch. The cross-correlation coefficient at each image sample is calculated to generate a matrix, and this matrix becomes the weighting factor. By summing data from these 2 receive apertures, we get the same data as from a uniformly weighted receive aperture. This RF data will then be weighted by the cross-correlation matrix. Instead of a 2-element alternating pattern as shown, any N-element alternating pattern can be used where N is less than half of the number of elements in the subaperture. The main difference between these configurations will be the location of the grating lobe. Increasing N will move the grating lobes closer to the mainlobe.
Fig. 3(d) 是一对接收孔径的示意图，其间距为一个波长 λ 。RX1 使用交替模式，即2个元素开，2个元素关。RX2 使用相反的交替模式，即2个元素关，2个元素开。这些接收孔径本质上是稀疏阵列，具有4个波长的间距。因此，预计在PSF中会出现光栅瓣。第 n 个光栅瓣的位置由

θn=sin−1(nλd),(3)

View Source\theta_{n}={\hbox{sin}}^{-1}\left({n\lambda\over d}\right),\eqno{\hbox{(3)}} 给出，其中 n 是第 n 个光栅瓣， λ 是超声波长， d 是元素间距或间距。在每个图像样本处计算互相关系数以生成矩阵，此矩阵成为加权因子。通过对这2个接收孔径的数据求和，我们得到与均匀加权接收孔径相同的数据。然后，这个射频数据将由互相关矩阵加权。如所示，不仅限于2元素交替模式，任何 N -元素交替模式都可以使用，其中 N 小于子孔径中元素数量的一半。这些配置之间的主要区别将是光栅瓣的位置。 增加 N 将使光栅瓣更接近主瓣。

We have performed computer simulations using Field II to generate lateral beamplots for all 4 designs [15]. A 5 MHz Gaussian pulse with 50% bandwidth was used as the transmit pulse and a delta function as the element impulse response. For a point target simulation, an RMS energy value was calculated from the received voltage trace. All RMS energy values were converted to decibels after normalizing to the maximum energy level. The transmit-and-receive focus was fixed at 30 mm for the point target simulation. Because there is rarely a point target in a clinical environment, we have also done a simulation using a cylindrical 3 mm diameter anechoic cyst located at 30 mm depth embedded in a 3-D phantom of scatterers. The parameters for the simulation are listed in Table I.
我们使用Field II进行了计算机模拟，为所有4种设计生成了横向波束图。作为发射脉冲，我们使用了一个5 MHz的高斯脉冲，带宽为50%，并使用了一个delta函数作为元素脉冲响应。对于点目标模拟，我们从接收到的电压迹线中计算了均方根能量值。所有均方根能量值在归一化到最大能量水平后被转换为分贝。点目标模拟的发射和接收焦点固定在30毫米。因为在临床环境中很少有点目标，我们还进行了一个模拟，使用了一个位于30毫米深度、嵌入在一个3-D散射体幻影中的直径为3毫米的无回声圆柱形囊肿。模拟的参数列在了。

Table I 1×128 Linear Array and Imaging Parameters.
表I 线性阵列和成像参数。

For our experimental setup, individual element RF signals were collected for off-line processing from an ATS spherical lesion phantom (Model 549, ATS Laboratories, Bridgeport, CT) containing a 3 mm anechoic cyst using an Ultrasonix Sonix RP ultrasound system (Ultrasonix Medical Corporation, Richmond, BC, Canada) having 40 MHz sampling frequency. This system has great flexibility allowing the researcher to control parameters such as transmit aperture size, transmit frequency, receive aperture, filtering, and time-gain compensation. In this experiment, a 128-element, 300 μm pitch, L14-5/38 linear array was used. A I-cycle transmit pulse of 5 MHz and an f−number=1.5 was used. In receive, element data was collected and receive beamforming was done off-line using Matlab (The MathWorks, Inc., Natick, MA). Dynamic receive focusing was used with focal updates every 0.1 mm. The image line spacing is 150 μm. Data from each channel were collected 32 times and averaged to minimize effects of electronic noise.
在我们的实验设置中，使用Ultrasonix Sonix RP超声系统（Ultrasonix Medical Corporation，加拿大不列颠哥伦比亚省里士满）从一个ATS球形病变模型（型号549，ATS实验室，康涅狄格州布里奇波特）收集了单个元素的射频信号，该模型包含一个3毫米的无回声囊肿，用于离线处理，该系统的采样频率为40 MHz。这个系统具有很大的灵活性，允许研究人员控制参数，如发射孔径大小、发射频率、接收孔径、滤波和时间增益补偿。在这个实验中，使用了一个128元素， 300 μm 间距，L14-5/38线性阵列。使用了一个5 MHz的1周期发射脉冲和一个 f−number=1.5 。在接收时，收集了元素数据，并使用Matlab（The MathWorks, Inc.，马萨诸塞州纳蒂克）进行了离线接收波束形成。使用了动态接收聚焦，每0.1毫米更新一次焦点。图像线间距为 150 μm 。为了最小化电子噪声的影响，每个通道的数据被收集了32次并进行了平均。

In an experimental setting as described above, an analog RF signal is digitized with a sampling frequency of 40 to 60 MHz. Additional simulations were done with 40 MHz delay quantization in transmit and receive beamforming to model our experimental setup. This introduces delay quantization error and gives us a better understanding of how DAX performs on a commercially available system.
在上述实验设置中，模拟射频信号以40至60 MHz的采样频率被数字化。额外的模拟在发射和接收波束形成中以40 MHz的延迟量化完成，以模拟我们的实验设置。这引入了延迟量化误差，并让我们更好地理解DAX在商用系统上的表现。

All signals in the experiments are bandpass filtered using a 64-tap finite impulse response (FIR) bandpass filter with frequency range limited to the −6 dB bandwidth of the transducer. After the signals are bandpass filtered, delayed, apodized, and summed to create RX1 and RX2, the 2 sets of data are cross-correlated. The cross-correlation value is sent to a thresholding operator. If the value is less than or equal to ε, or 0.001 in our case, then the value is replaced with 0.001. If it is greater than 0.001, then the value remains unchanged. A second filter, which has the same passband window as the first filter, might be required to reduce sharp discontinuities in images that might be caused by multiplication of the weighting matrix. The Hilbert transform is used for envelope detection, and all images are displayed on a log scale.
在实验中，所有信号都使用64阶有限脉冲响应（FIR）带通滤波器进行带通滤波，频率范围限制在换能器的-6 dB带宽内。信号经过带通滤波、延迟、调制和求和后，创建了RX1和RX2，这两组数据被进行互相关。互相关值被发送到一个阈值操作器。如果该值小于或等于0.001（在我们的案例中），则该值被替换为0.001。如果它大于0.001，则该值保持不变。可能需要第二个滤波器，其通带窗口与第一个滤波器相同，以减少可能由权重矩阵乘法引起的图像中的尖锐不连续性。希尔伯特变换用于包络检测，所有图像都以对数尺度显示。

We have presented our dual apodization with cross-correlation (DAX) technique that suppresses sidelobes and lowers clutter, thus improving CNR, without compromising spatial resolution in ultrasound imaging. The main idea behind this method is to use a pair of apodization schemes that are highly cross-correlated in the mainlobe but have low or negative cross-correlation in the sidelobe region. DAX uses 2 sets of beamformed data acquired with 2 different receive apertures and cross-correlates segments of RF data. This cross-correlation matrix serves as a pixel-by-pixel weighting function that will be multiplied to the minimum or to the sum of the 2 data sets. Theory and simulation were validated in ultrasound tissue-mimicking phantoms where contrast improvement in terms of CNR was 139% in simulation and 123% experimentally. Lateral and axial resolution are not sacrificed to improve CNR. The alternating pattern showed the highest CNR experimentally. This alternating pattern purposely creates 2 sets of grating lobes, which are 180° out of phase with respect to each other. Although grating lobes have long been a potential source for clutter in ultrasound imaging, DAX uses gratings lobes to help distinguish between mainlobe and clutter signals.
我们提出了一种双重孔径加权与互相关技术（DAX），该技术通过抑制旁瓣和降低杂波来改善对比度噪声比（CNR），同时不损害超声成像中的空间分辨率。这种方法的主要思想是使用一对孔径加权方案，这些方案在主瓣中高度互相关，但在旁瓣区域具有低或负互相关。DAX使用两组通过两个不同接收孔径获取的波束形成数据，并对射频数据的段进行互相关。这个互相关矩阵作为逐像素加权函数，将乘以两个数据集的最小值或总和。理论和模拟在超声组织模拟体中得到了验证，其中对比度改善方面的CNR在模拟中提高了139%，在实验中提高了123%。横向和轴向分辨率没有牺牲以改善CNR。交替模式在实验中显示出最高的CNR。这种交替模式故意创建了两组互为180°相位差的光栅瓣。 尽管光栅叶片长期以来一直是超声成像中杂波的潜在来源，但DAX利用光栅叶片来帮助区分主瓣和杂波信号。

Occasionally, DAX will add artificial dark spots in the speckle region. In fact, the DAX algorithm slightly lowers the speckle SNR, defined as the ratio of mean to standard deviation of the scattered signal for fully developed speckle, by 4 to 11%. The SNR in the speckle region before applying the DAX algorithm was 1.91. The SNR in the speckle region after the DAX algorithm was applied were 1.81, 1.70, 1.84, and 1.77 for uniform-Hanning, common midpoint, random, and alternating pattern, respectively. In cystic regions, it may be possible that clutter signals will have a high cross-correlation coefficient. In this situation, minimal or no improvement in contrast will be seen. The occurrence of both of these artifacts could be minimized by several straightforward options. Using a moving average or median filter on the cross-correlation coefficients is one approach. Because this process is a smoothing of the weighting matrix, the speckle pattern is not smeared. We have also briefly investigated the effect of correlation window on the cyst. A longer correlation window produced a poorly delineated cyst but with fewer dark spots in the speckle region. If the window size was too small, the speckle had more pits due to greater variation in cross-correlation coefficients. Empirically, 20 to 30 samples, which is roughly 2 wavelengths, performed best in terms of CNR. Finally, the threshold and weighting as a function of ρ could be adjusted. All these methods may help eliminate dark spots but may also lower CNR. This will be investigated in future work.
偶尔，DAX会在斑点区域添加人造暗点。实际上，DAX算法稍微降低了斑点的信噪比（SNR），即全面发展斑点的散射信号的平均值与标准差的比率，降低了4到11%。应用DAX算法前，斑点区域的SNR为1.91。应用DAX算法后，斑点区域的SNR分别为均匀-汉宁、共同中点、随机和交替模式的1.81、1.70、1.84和1.77。在囊性区域，杂波信号可能会有高的互相关系数。在这种情况下，对比度的改善可能微乎其微或没有改善。这两种伪影的出现都可以通过几种简单的方法最小化。一种方法是对互相关系数使用移动平均或中位数滤波。因为这个过程是权重矩阵的平滑处理，所以不会模糊斑点图案。我们还简要研究了相关窗口对囊肿的影响。较长的相关窗口产生了轮廓不清的囊肿，但在斑点区域的暗点较少。 如果窗口尺寸太小，由于交叉相关系数的变化较大，散斑会有更多的凹点。经验表明，20到30个样本，大约2个波长，在对比噪声比方面表现最佳。最后，可以调整阈值和作为 ρ 函数的加权。所有这些方法可能有助于消除暗点，但也可能降低对比噪声比。这将在未来的工作中进行研究。

Preliminary attempts with 1-D lateral cross-correlation gave us a slightly lower CNR than using 1-D axial crosscorrelation; 2-D cross-correlation gave us a comparable improvement to 1-D axial cross-correlation but with increased computational load. This also requires further investigation.
初步尝试使用一维横向互相关给我们带来的对比噪声比略低于使用一维轴向互相关；二维互相关给我们带来了与一维轴向互相关相当的改进，但增加了计算负担。这还需要进一步研究。

One limitation of the current DAX algorithm is that it does not improve contrast of hyper-echoic or hypo-echoic lesions because signals are well-correlated inside and outside the lesions. A more generalized DAX algorithm that adjusts the weighting as a function of cross-correlation is under investigation to improve contrast of hyper-echoic or hypo-echoic targets. It is also interesting to note that the weighting matrix in Fig. 9 clearly identifies the cyst. This weighting matrix itself could possibly be used as a speckle free image. Additional work is needed to verify the feasibility of the cross-correlation based image for a variety of targets. Work is also underway to investigate the application of this technique to suppress sidelobes in other ultrasound technologies such as high frequency ultrasound, photoacoustic imaging, and 3-D ultrasound [17]–​[19]. Also in future work, we will examine the robustness of this technique in the presence of low signal-to-noise ratios and aberrating layers. Finally, we believe that DAX is relatively computationally inexpensive because a matrix of cross-correlation coefficients at only zero lag needs to be calculated on a 21-sample segment of RF data at 40 MHz sampling frequency. This would allow DAX to be easily implemented on a commercial real-time ultrasound system.
当前DAX算法的一个限制是它无法改善高回声或低回声病变的对比度，因为病变内外的信号相关性很高。正在研究一种更通用的DAX算法，该算法通过作为互相关函数调整权重来改善高回声或低回声目标的对比度。同样值得注意的是，权重矩阵清楚地识别出了囊肿。这个权重矩阵本身可能就可以作为一个无斑点的图像。需要进一步的工作来验证基于互相关的图像对各种目标的可行性。还在进行的工作包括探索将这项技术应用于抑制其他超声技术中的旁瓣，如高频超声、光声成像和三维超声。在未来的工作中，我们还将检验这项技术在低信噪比和异常层存在时的稳健性。 最后，我们认为DAX在计算上相对不昂贵，因为只需要在40 MHz采样频率下的21个样本段的RF数据上计算一个零延迟的交叉相关系数矩阵。这将使得DAX能够轻松地在商业实时超声系统上实现。