## 3 Research Method  
The aforementioned four beamforming methods for multi-angle PW imaging are compared using the data on the PICMUS platform established for IEEE IUS 2016 [27] to quantitatively evaluate the resolution and contrast on two simulated phantoms and two experimental phantoms, respectively. In vivo data of a carotid artery in both the transverse and longitudinal views are also included. The data are acquired using a 128-element linear array with a pitch of 0.3 mm. The transmit waveform is a 2.5-cycle sinusoid at 5.2 MHz. The received echo is digitized at a sampling frequency of 20.8 MHz. The detailed parameters of the PICMUS dataset are listed in Table 1. The performances are evaluated with seven PW compounding (7 PW), uniformly tilted from \(-16^{\circ}\) to \(+16^{\circ}\) with spacing of \(5.3^{\circ}\). The mean resolutions of the image are automatically measured by the PICMUS program using Matlab (R2018b, The MathWorks, Natick, MA, USA) in terms of the full widths at half maximum (FWHM) of wire reflectors in Figure 1a-d and Figure 3a-d. The FWHMs in the axial and lateral directions are respectively referred to axial width (AW) and lateral width (LW) in this paper. The ghost-artifact level is estimated as the image magnitude in the background area (red rectangle) in Figure 1a. Note that the ghost artifact in this study mainly comes from the axial lobes and grating lobes of the horizontal wire reflectors at depths of 20 mm. The contrast ratio (CR) and contrast-to-noise ratio (CNR) are calculated using the image magnitude before log-compression inside the cyst (green circle) and in the background region (blue rectangle) in Figure 1e and Figure 3e as follows:  
\[\text{CR}=20\log_{10}(\mu_{cyst}/\mu_{bck}) \tag{7}\]  
\[\text{CNR}=\Big{|}\mu_{cyst}-\mu_{bck}\Big{|}/\sqrt{\sigma_{cyst}^{2}+\sigma _{bck}^{2}} \tag{8}\]  
where \(\mu_{cyst}\), \(\mu_{bck}\), \(\sigma_{cyst}\), and \(\sigma_{bck}\) are the averaged values and the standard deviations of image magnitude, respectively, in the cyst and the background. In addition to the conventional CR and CNR, the generalized CNR (GCNR) as suggested in Reference [28] is also included for evaluation of image contrast. The GCNR is estimated from the overlap area of the probability density function of the background and the cyst regions subtracted from unity. In order to perform baseband beamforming, the IQ channel data and corresponding program are adopted on the PICMUS platform. Specifically, the received channel waveforms are firstly demodulated and then down-sampled by a factor of four. Given the baseband IQ channel data from individual PW transmissions, time compensations and phase rotations are performed for every image pixel. Then, all phase-aligned channel data from seven PW transmissions are concatenated to construct the echo matrix. For 2D-DAS beamforming, the echo matrix is sequentially summed in the dimension of the PW transmit angle and then in the dimension of the receiving channel to generate the final image. For 2D-DMAS, Rx-DMAS, and Tx-DMAS beamforming, they are implemented according to Equations (3)-(5) in Section 2, respectively. Since the output of either beamforming method is still a baseband signal, the B-mode image in this study is reconstructed by simply taking the absolute value of the \begin{table}
\begin{tabular}{c c c c} \hline Max. PW angle & \(\pm 16^{\circ}\) & Number of PW angle & 7 \\ Element pitch & 0.3 mm & Element height & 5 mm \\ Element width & 0.27 mm & Elevation focus & 20 mm \\ Number of elements & 128 & Excitation & 2.5 cycle \\ Center frequency & 5.2 MHz & Sampling frequency & 20.8 MHz \\ Attenuation coefficient & 0.5 dB/(MHz\(\cdot\)cm) & Sound velocity & 1540 m/s \\ \hline \end{tabular}
\end{table} 
Table 1: Imaging parameters of PICMUS data. beamforming output to retrieve the envelope before log-compression with a dynamic range of 60 dB. In this study, \(p\) values of 1.5, 2.0, 2.5, and 3.0 are considered for all DMAS beamforming for quantitative comparison of image quality.