## 2 Materials and Methods
### Experimental Design
#### 2.2.3 Transmission Sequences  
Two of the transmission sequences were standard linear three-angle single transmit sequences (sTx3, \(\{-5,0,5\}\)) or seven-angle single transmit sequences (sTx7, \(\{-5:5/3:5\}\)). The third sequence was a double transmit sequence using 3 angles and, therefore, was composed of 6 transmits (dTx6, \(\{-5,-5,0,0,5,5\}\)). In each case, an odd number of angles was chosen to include the 0-degree steered transmit, which is least susceptible to grating lobes. Under this constraint, the sTx7 dataset was chosen to be a partial control for the sequence duration. Each dataset was processed using the LRIs and HRIs using the lag-one estimator described in Section 2.1.5. For the HRIs, a standard sixth order infinite impulse response filter (IIR) Butterworth filter was used for clutter filtering, with a slow-time cutoff frequency of 500 Hz (\(\approx\)24.6 mm/s). The cutoff frequency of this filter was chosen to compensate for the slow transition band of the Butterworth filter, which takes approximately 300 Hz to reach a 60-dB attenuation level. For the LRIs, clutter filtering was performed on the matched angle LRI channels as described in Section 2.1.4, with similarly designed specifications at the appropriately reduced sample rates as shown in Figure 4. This design decision resulted in a periodic notching effect, in accordance with multirate signal processing theory [14; 15]. The expected Nyquist velocities for each of these approaches are given in Table 2, in addition to other relevant slow-time quantities. In addition to the traditional approaches described above, the dTx6 dataset also was post processed using the pairwise (PW) methods described in Sections 2.1.6 (dTx6 LRI PW) and 2.1.7 (dTx6 HRI PW). The baseline averaging interval for each processing scheme was chosen to be around 1 ms in each case. Because the frame rate of the autocorrelation sequence varied so much across all the different processing schemes, matching the averaging schemes exactly was not possible. Furthermore, to avoid introducing half sample lags, odd length averages were used  
Figure 3: Experimental Setup. A linear 128-element linear array transducer was submerged in a degassed water bath and aligned with a hyperechoic rotation phantom. A layer of sound absorbing material (Sorbothane Inc., Kent, OH, USA) was used to suppress reverberation echoes from the edge of the plastic container. to keep the sequences temporally synchronized. These decisions resulted in the slight variations in the averaging interval as shown in Table 2.  
In addition to the color flow Doppler images, power Doppler images were also generated to help visualize the spatial energy distributions. These images were generated by calculating the mean-square value of the slow-time signal over the entire slow-time dimension, which was then converted to a decibel scale, such that  
\[P(\vec{r})=10\log_{10}\left(\frac{1}{N}\sum_{n=0}^{N-1}s(\vec{r},n\Delta t)^{2 }\right), \tag{22}\]  
where \(P(\vec{r})\) is the power Doppler signal at the location \(\vec{r}\), \(N\) is the total number of slow-time samples, and \(s(\vec{r},t)\) is the slow-time signal for either the LRIs or HRIs as appropriate. Note that in the LRI case, we do not evaluate the power Doppler on the individual polyphase channels, but rather the full slow-time signal. For the pairwise estimation schemes, no power Doppler images were produced due to lack of a relevant metric which accounts for the pairwise nature of the signals. In practice, the LRI power Doppler could serve as a relevant metric for the pairwise approaches for the purposes of stationary clutter suppression. As a ground truth for comparison purposes, a rotation model was fit to the data. Using a B-Mode image as a reference, points along the phantom boundaries were manually selected, and the centroid was computed.