## 3 Results  
### Flow Phantom Study  
Figure 6 shows the B-mode versus H-scan image of the flow phantom with a blood concentration of 50%. More specifically, Figure 7 shows the imaging results of each RGB channel in the H-scan image. The \(\text{G}H_{2}\) convolution outputs in the R channel shows a higher signal strength in the homogeneous phantom, while the signal in the vascular graft is small. The \(\text{G}H_{8}\) convolution outputs in the B channel maintain a high signal intensity in all regions. The result of the G channel corresponds to the conventional B-mode image without logarithmic compression. According to the definition of the H-scan, we can roughly assume that blue represents the contribution of relatively small scatterers, while red represents the contribution of relatively large scatterers. To further illustrate that H-scan signals in the vascular graft are mostly contributed by small scatterers, a 1.5-mm \(\times\) 1.5-mm ROI in the center of the vascular graft (yellow dashed square) was selected to evaluate the changes in the signal strength of R channels and B channels at different concentrations of blood.  
Figure 5: (**a**) Power Doppler image of the in vivo rabbit brain using the proposed H-doppler. (**b**) A zoomed image of the brain blood flow signal. The white dashed region indicates the data processing Region of Interest (ROI) for the contrast-to-noise-ratio (CNR) evaluation, with the vessels manually selected and indicated by white lines and the rest of the signal within the white dashed ROI regarded as the background clutter signal. The green dashed box indicates the background noise ROI.  
Figure 6: B-mode image (upper image) and H-scan ultrasound image (lower image) of the flow phantom at a blood concentration of 50%. The color blue in the H-scan image is contributed by relatively small scatterers, and the red represents the opposite.  
Figure 7: The images of the envelopes of the normalized R-channel data (GH\({}_{2}\) convolution outputs for large layer scattering), B-channel data (GH\({}_{\delta}\) convolution outputs for Rayleigh scattering) and G-channel data [original Radio Frequency (RF) data]. The vascular graft is highlighted by the white dashed lines, and a 1.5-mm \(\times\) 1.5-mm ROI (yellow dashed square) is selected to evaluate the signal strength of R channel and B channel.  
Figure 8 shows the R and B channel mean intensities of the bovine blood solution in ROI with concentrations ranging from 0% to 100%. With a blood concentration of 0 (pure water), small mean intensity values (<0.05) were gauged in both R-channels and B-channels instead of 0, as expected. We believe this is due to the inevitable introduction of air bubbles in the bovine blood solution during the experiment. When the blood concentration increased, one can see that there was no significant increase in the R channel mean intensity, which corresponded to the large layer scattering, whereas the intensity of the B channel increased rapidly, as expected. This suggests that a power Doppler imaging method based on G\(H_{2}\) convolution outputs, which is mainly contributed by the Rayleigh scattering of red blood cells, could potentially improve the sensitivity of blood flow detection.